Methods and systems for controllably moving multiple moveable stages in a displacement device

ABSTRACT

Aspects of the invention provide methods and systems for moving a plurality of moveable stages relative to a stator. The stator comprises a plurality of coils shaped to provide pluralities of coil trace groups where each coil trace group comprises a corresponding plurality of generally linearly elongated coil traces which extend across a stator tile. Each moveable stage comprises a plurality of magnet arrays. Methods and apparatus are provided for moving the moveable stages relative to the stator, where a magnet array from a first moveable stage and a magnet array from a second moveable stage both overlap a shared group of coil traces. For at least a portion of the time that the magnet arrays from the first and second moveable stages overlap the shared group of coil traces, currents are controllably driven in the shared coil trace group based on the positions of both the first and second moveable stages. The positions of the first and second moveable stages may be ascertained by feedback.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/881,719 entitled METHODS AND SYSTEMS FOR CONTROLLABLY MOVING MULTIPLEMOVEABLE STAGES IN A DISPLACEMENT DEVICE filed 26 Jan. 2018, which is acontinuation of U.S. application Ser. No. 15/370,987 (now U.S. Pat. No.10,056,816) entitled METHODS AND SYSTEMS FOR CONTROLLABLY MOVINGMULTIPLE MOVEABLE STAGES IN A DISPLACEMENT DEVICE and having a filingdate of 6 Dec. 2016, which is, in turn, a continuation of PatentCooperation Treaty (PCT) application No. PCT/CA2015/050523 entitledMETHODS AND SYSTEMS FOR CONTROLLABLY MOVING MULTIPLE MOVEABLE STAGES INA DISPLACEMENT DEVICE and having an international filing date of 5 Jun.2015, which, in turn, claims the benefit of the priority of U.S.application No. 62/009165 entitled DISPLACEMENT DEVICES AND METHODS FORFABRICATION, MEASUREMENT, USE AND CONTROL OF SAME and have a filing dateof 7 Jun. 2014. U.S. application Ser. Nos. 15/881,719, 15/370,987, PCTapplication No. PCT/CA2015/050523 and US application No. 62/009165 areall hereby incorporated herein by reference.

TECHNICAL FIELD

The invention relates to displacement devices. Particular embodimentsprovide systems and corresponding methods for moving multiple movablestages relative to a stator.

BACKGROUND

Motion stages (XY tables and rotary tables) are widely used in variousmanufacturing, inspection and assembling processes. A common solutioncurrently in use achieves XY motion by stacking two linear stages (i.e.a X-stage and a Y-stage) together via connecting bearings.

A more desirable solution involves having a single moving stage capableof XY motion, eliminating additional bearings. It might also bedesirable for such a moving stage to be able to provide at least some Zmotion. Attempts have been made to design such displacement devicesusing the interaction between current-carrying coils and permanentmagnets. Examples of efforts in this regard include the following: U.S.Pat. Nos. 6,003,230; 6,097,114; 6,208,045; 6,441,514; 6,847,134;6,987,335; 7,436,135; 7,948,122; US patent publication No. 2008/0203828;W. J. Kim and D. L. Trumper, High-precision magnetic levitation stagefor photolithography. Precision Eng. 22 2 (1998), pp. 66-77; D. L.Trumper, et al, “Magnet arrays for synchronous machines”, IEEE IndustryApplications Society Annual Meeting, vol. 1, pp. 9-18, 1993; and J. W.Jansen, C. M. M. van Lierop, E. A. Lomonova, A. J. A. Vandenput,“Magnetically Levitated Planar Actuator with Moving Magnets”, IEEE Tran.Ind. App., Vol 44, No 4, 2008.

More recent techniques for implementing displacement devices having amoveable stage and a stator are described in:

-   -   PCT application No. PCT/CA2012/050751 (published under        WO/2013/059934) entitled DISPLACEMENT DEVICES AND METHODS FOR        FABRICATION, USE AND CONTROL OF SAME; and    -   PCT application No. PCT/CA2014/050739 (published under        WO/2015/017933) entitled DISPLACEMENT DEVICES AND METHODS AND        APPARATUS FOR DETECTING AND ESTIMATING MOTION ASSOCIATED WITH        SAME.

There is a general desire to provide displacement devices havingcharacteristics that improve upon those known in the prior art. One areawhere there is room for improvement over existing displacement devicesis in the controllable movement of multiple (two or more) moveablestages in a displacement device (e.g. relative to a single stator). Itwill be appreciated that there are multiple applications where it may bedesirable (e.g. for efficiency or any other reasons) why it might beadvantageous to be able to move multiple moveable stages in adisplacement device. A challenge associated with controllably movingmultiple moveable stages in a displacement device involvescross-coupling between the forces generated to move the multiplemoveable stages. For example, forces generated by the displacementdevice to move a first moveable stage may cross-couple into one or moreother moveable stages. There is a desire to move multiple moveablestages in a displacement device.

The foregoing examples of the related art and limitations relatedthereto are intended to be illustrative and not exclusive. Otherlimitations of the related art will become apparent to those of skill inthe art upon a reading of the specification and a study of the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments are illustrated in referenced figures of thedrawings. It is intended that the embodiments and figures disclosedherein are to be considered illustrative rather than restrictive.

FIGS. 1A and 1B (together, FIG. 1) respectively depict a schematicpartially cut-away top view and side cross-sectional views of adisplacement device according to a particular embodiment of theinvention.

FIG. 2 is a top view of a displacement device which comprises aplurality of moveable stages.

FIGS. 3A and 3B are each a schematic top view of a magnet array assemblycomprising a plurality of elongated segment magnet arrays according to aparticular embodiment. FIG. 3C is a cross-sectional view of an exemplaryy-magnet array which is used in the FIG. 3A magnet array assembly andwhich could be used for the magnet array assemblies of FIG. 3B or any ofthe other elongated segment magnet array assemblies described herein.

FIG. 4 is a partial schematic side cross-sectional view of adisplacement device according to a particular embodiment of theinvention.

FIG. 5 shows a schematic top view of a stator coil assembly according toa particular embodiment which may be used in any of the displacementdevices described herein.

FIGS. 6A-6C each show schematic depictions of portions of coil tracelayers and/or coil traces in a corresponding excitation region.

FIG. 7 is a schematic top view of the FIG. 1 displacement deviceincorporating a moveable stage having the FIG. 3B magnet array assemblyaccording to a particular embodiment.

FIGS. 8A and 8B are respectively a schematic block diagram of a controlsystem suitable for use in controlling any of the displacement devicesdescribed herein according to a particular embodiment and one possibleconnection scheme to connect a group of y-traces in one coil trace layerwithin an excitation region according to a particular embodiment.

FIG. 9 is a partial schematic isometric view of a displacement devicecomprising a feedback sensing system according to a particularembodiment of the invention.

FIG. 10A is a schematic depiction of moveable stage and a magnet arrayassembly according to a particular embodiment. FIG. 10B shows an x-tracelayer corresponding to a stator tile (excitation region) of a statoraccording to a particular embodiment. FIG. 10C shows a y-trace layercorresponding to the stator tile (excitation region) of the FIG. 10Bstator according to a particular embodiment. FIG. 10D is a schematicdepiction of the entire stator tile incorporating the FIG. 10B x-tracelayer and the FIG. 10C y-trace layer. FIG. 10E is a cross-sectional viewof one of the y-magnet arrays of the FIG. 10A magnet array assembly.

FIG. 11A shows a position sensing layer corresponding to a stator tile(excitation region) of the FIG. 10 stator. FIG. 11B shows a side of astator tile, which includes a position sensing layer atop a number ofcoil trace layers according to a particular embodiment.

FIG. 12 shows a non-limiting embodiment of a displacement deviceaccording to the FIG. 10 embodiment, which comprises a plurality ofmoveable stages and a plurality of stator tiles (excitation regions).

FIGS. 13A-13G (collectively, FIG. 13) illustrate a method for movingfirst and second moveable stages of the FIG. 10 displacement device topass one another in a stator lane having a width of a single tile (or topass one another on a single tile) according to a particular embodiment.

FIGS. 14A and 14B respectively show queuing formations for multiplemoveable stages of the FIG. 10 displacement device and methods formoving moveable stages into and out of such queuing formations accordingto particular embodiments.

DESCRIPTION

Throughout the following description specific details are set forth inorder to provide a more thorough understanding to persons skilled in theart. However, well known elements may not have been shown or describedin detail to avoid unnecessarily obscuring the disclosure. Accordingly,the description and drawings are to be regarded in an illustrative,rather than a restrictive, sense.

Aspects of the invention provide methods and systems for moving aplurality of moveable stages relative to a stator. The stator comprisesa plurality of coils shaped to provide pluralities of coil trace groupswhere each coil trace group comprises a corresponding plurality ofgenerally linearly elongated coil traces which extend across a statortile. Each moveable stage comprises a plurality of magnet arrays.Methods and apparatus are provided for moving the moveable stagesrelative to the stator, where a magnet array from a first moveable stageand a magnet array from a second moveable stage both overlap a sharedgroup of coil traces. For at least a portion of the time that the magnetarrays from the first and second moveable stages overlap the sharedgroup of coil traces, currents are controllably driven in the sharedcoil trace group based on the positions of both the first and secondmoveable stages. The positions of the first and second moveable stagesmay be ascertained by feedback.

Aspects of the invention provide displacement devices which comprise astator and one or more moveable stages. For brevity, moveable stages mayalso be referred to herein as movers. The stator comprises a pluralityof electrically conductive coils shaped to provide pluralities ofgenerally linearly elongated coil traces. Each moveable stage may bemoveable relative to the stator within a two-dimensional working regionof the displacement device. Each moveable stage may comprise one or moremagnet arrays. In some embodiments, each magnet array comprises aplurality of magnetization segments, where each magnetization segmenthas a corresponding magnetization direction. Each magnet array maycomprise at least two magnetization segments with differentmagnetization directions. One or more amplifiers may be connected todrive a plurality of currents in the plurality of coil traces. Acontroller may be connected to deliver control signals to the one ormore amplifiers. The control signals may be used to control currentdriven by the one or more amplifiers into at least some of the pluralityof coil traces. The currents controllably driven into the at least someof the plurality of coil traces create magnetic fields which causecorresponding magnetic forces on the one or more magnet arrays of themoveable stage, thereby moving the moveable stage relative to the stator(e.g. within the working region). In some embodiments, the magneticforces associated with the interaction between the magnetic fieldscreated by the currents in the at least some of the coil traces and themagnetic fields associated with the magnet arrays may attract themoveable stage toward the stator at all times when the controller iscontrolling the currents driven by the one or more amplifiers. In someembodiments, the magnetic forces associated with the interaction betweenthe magnetic fields created by the currents in the at least some of thecoil traces and the magnetic fields associated with the magnet arraysmay force the moveable stage away from the stator to balancegravitational forces with an air gap at all times when the controller iscontrolling the currents driven by the one or more amplifiers.

FIGS. 1A and 1B (together FIG. 1) respectively depict a partiallycut-away top view and a side cross-sectional view of a displacementdevice 50 according to a particular embodiment. Displacement device 50comprises a stator 30, a moveable stage 10, a controller 60 and one ormore amplifiers 70. Moveable stage 10 may be controllably moved relativeto stator 30 about a working region 36 of displacement device 50.

For purposes of describing the displacement devices disclosed herein, itcan be useful to define a pair of coordinate systems—a stator coordinatesystem which is fixed to the stator (e.g. to stator 30 of FIG. 1A); anda stage coordinate system which is fixed to the moveable stage (e.g.moveable stage 10 of FIG. 1A) and moves with the moveable stage relativeto the stator and the stator coordinate system. This description may useconventional Cartesian coordinates (x, y, z) to describe thesecoordinate systems, although, it will be appreciated that othercoordinate systems could be used. For convenience and brevity, in thisdescription and the associated drawings, the directions (e.g. x, y, zdirections) in the stator coordinate system and the directions in thestage coordinate system may be shown and described as being coincidentwith one another—i.e. the stator-x, stator-y and stator-z directions maybe shown as coincident with stage-x, stage-y and stage-z directions,respectively. Accordingly, this description and the associated drawingsmay refer to directions (e.g. x, y, and/or z) to refer to directions inboth or either of the stator and stage coordinate systems. However, itwill be appreciated from the context of the description herein that insome embodiments and/or circumstances, the moveable stage (e.g. moveablestage 10) may move relative to the stator (e.g. stator 30) such thatthese stator and stage directions are no longer coincident with oneanother. In such cases, this disclosure may adopt the convention ofusing the terms stator-x, stator-y and stator-z to refer to directionsand/or coordinates in the stator coordinate system and the termsstage-x, stage-y and stage-z to refer to directions and/or coordinatesin the stage coordinate system. In this description and the associateddrawings, the symbols Xm, Ym and Zm may be used to refer respectively tothe stage-x, stage-y and stage-z directions, the symbols Xs, Ys and Zsmay be used to refer respectively to the stator-x, stator-y and stator-zdirections and the symbols X, Y and Z may be used to refer respectivelyto either or both of the stage-x, stage-y and stage-z and/or stator-x,stator-y and stator-z directions. In some embodiments, during normaloperation, the stage-z and stator-z directions are approximately in thesame direction (e.g. within ±30° in some embodiments; within ±10° insome embodiments; and within ±2° in some embodiments).

In some embodiments, the stator-x and stator-y directions arenon-parallel. In particular embodiments, the stator-x and stator-ydirections are generally orthogonal. In some embodiments, the stage-xand stage-y directions are non-parallel. In particular embodiments, thestage-x and stage-y directions are generally orthogonal.

Controller 60 and amplifiers 70 may be configured and connected forcontrollably moving moveable stage 10 relative to stator 30 in workingregion 36. For example, controller 60 may be configured to generatecontrol signals and connected to provide such control signals toamplifiers 70. Amplifiers 70 may be connected to drive currents in coiltraces 32, 34. In response to the control signals from controller 60,amplifiers 70 may drive current in coil traces 32, 34 of stator 30 toeffect movement of moveable stage 10 relative to stator 30.In someembodiments, controller 60 is configured to move moveable stage 10 to adesired position, (x_(r), y_(r)), within working region 36, where x_(r)is a desired position of moveable stage 10 in the stator-x direction andy_(r) is a desired position of the moveable stage in the stator-ydirection. Unless the context dictates otherwise, throughout thisdisclosure and the accompanying claims, when referring to a position ofa moveable stage, a location of a moveable stage, movement of a moveablestage generally within a working region and/or the like, such position,location, movement and/or the like should be understood to refer to theposition, location, movement and/or the like of a reference point on themoveable stage. Such reference point may be, but is not limited to, apoint at the center of the magnet array assembly of the moveable stage.Such reference point could be some other location on the moveable stage.Generally, the desired position (x_(r), y_(r)) is a function of time, t,and represents where a moveable stage should be ideally located at eachtime, t.

The FIG. 1 displacement device 50 and its components (e.g. moveablestage 10, stator 30, controller 60, amplifiers 70 and/or the like)represent generalized embodiments of a displacement device and itscomponents which is useful for describing the principles of operation ofdisplacement devices according to the various embodiments describedherein. Further embodiments of displacement devices and/or theircomponents described herein may use similar reference numerals (e.g.with a preceding digit, a trailing symbol, a trailing letter and/or atrailing number) to those used to describe displacement device 50 and/orits components. Unless the context or description dictates otherwise,such displacement devices and/or their components may exhibit featuresand/or characteristics which may be similar to the features andcharacteristics of displacement device 50 and/or its components (or viceversa). For example, moveable stages 110A, 210_2 described in moredetail below are moveable stages according to particular embodiments ofthe invention. Unless the context or description dictates otherwise,moveable stages 110A, 210_2 may have features and/or characteristicssimilar to those discussed herein for moveable stage 10 (or vice versa).As another example, stators 130, 230 described in more detail below arestators according to particular embodiments of the invention. Unless thecontext or description dictates otherwise, stators 130, 230 may havefeatures and/or characteristics similar to those discussed herein forstator 30. Further, unless the context or description dictatesotherwise, it should also be understood that when referring to featuresand/or characteristics of displacement device 50 and/or its components,the corresponding description should be understood to apply to any ofthe particular embodiments of displacement devices and/or theircomponents.

Moveable Stage

In the FIG. 1 embodiment, displacement device 50 is shown with a singlemoveable stage 10. In general, however, displacement device 50 maycomprise a plurality of moveable stages, each of which may be similar tomoveable stage 10 and each of which may be controlled by controller 60using amplifier(s) 70 to drive currents in coil traces 32, 34 asdescribed herein. FIG. 2 shows a top view of displacement device 50′,which comprises a plurality (e.g. two) moveable stages 10A, 10B.Controller 60 may be configured to generate control signals forcontrollably moving both moveable stages 10A, 10B. In other respects,displacement device 50′ may be substantially similar to the FIG. 1displacement device 50. By way of non-limiting example, each of moveablestages 10A, 10B may have similar features and/or characteristics tomoveable stage 10 of displacement device 50 and stator 30 ofdisplacement device 50′ may have similar features and/or characteristicsto stator 30 of displacement device 50. FIG. 2 shows that moveablestages 10A, 10B need not be aligned with one another. Consequently, eachmoveable stage 10A, 10B may be described using its own correspondingstage coordinate system. In the case shown in FIG. 2, the stagedirections X_(m1)/Y_(m1)/Z_(m1) define the stage coordinate system formoveable stage 10A and the stage directions X_(m2)/Y_(m2)/Z_(m2) definethe stage coordinate system for moveable stage 10B. Displacement device50′ can be built to operate with any suitable number of moveable stages10. In some embodiments, displacement device 50′ comprises threemoveable stages. In some embodiments, displacement device 50′ maycomprise dozens to hundreds of moveable stages. In some embodimentsstill, displacement device 50′ may comprise thousands of moveablestages.

Referring back to FIG. 1, moveable stage 10 comprises a magnet arrayassembly 16 which comprises one or more magnet arrays 12. Magnet arrayassembly 16 should be understood to comprise the combination of the oneor more individual magnet arrays 12. Each magnet array 12 may comprise acorresponding plurality of magnetization segments 14A, 14B, 14C, 14D . .. (collectively, magnetization segments 14), each magnetization segment14 having a corresponding magnetization direction. In some embodiments,the magnetization segments 14 of a particular magnet array 12 have atleast two magnetization directions that are different from one another.In the FIG. 1 embodiment, moveable stage 10 comprises a first magnetarray 12 having a plurality of corresponding first magnetizationsegments 14. Moveable stage 10 may be located adjacent to (e.g. atop)stator 30. As discussed above, in some embodiments, moveable stage 10may be attracted toward (and bear against) stator 30 when controller 60is controlling the currents driven by amplifiers 70; and, in someembodiments, moveable stage 10 is forced away from stator 30 (e.g. toprovide an air gap between stator 30 and moveable stage 10) whencontroller 60 is controlling the currents driven by amplifiers 70. Inthe illustrated embodiment, for the sake of generality, moveable stage10 comprises an optional stage bearing surface 24 that is generallyplanar (with a normal in the stage-z direction) and which may bearagainst an optional stator bearing surface 26 that is generally planar(with a normal in the stator-z direction) in embodiments where moveablestage is attracted toward stator 30.

One type of magnet array assembly 16 that can be used with any of thedisplacement devices disclosed herein is referred to as an elongatedsegment magnet array assembly 16. An elongated segment magnet arrayassembly 16 comprises one or more elongated segment magnet arrays 12,wherein each such magnet array 12 comprises plurality of linearlyelongated magnetization segments 14 (e.g. elongated in a stage-xdirection or a stage-y direction), with each magnetization segment 14having a corresponding magnetization direction that is generallyorthogonal to its elongation direction. At least two of themagnetization segments 14 in each magnet array 12 may have magnetizationdirections that are different from one another.

In some embodiments, moveable stage 10 comprises an elongated segmentmagnet array 16 which in turn comprises four elongated segment magnetarrays 12 (first, second, third and fourth magnet arrays 12). A firstmagnet array 12 in such an elongated segment magnet array assembly 16may comprise a plurality of linearly elongated first magnetizationsegments 14 (e.g. elongated in a stage-x direction), with each firstmagnetization segment 14 having a corresponding magnetization directionthat is generally orthogonal to the stage-x direction. At least two ofthe first magnetization segments 14 may have magnetization directionsthat are different from one another. The first magnetization directionsof the first magnetization segments 14 may exhibit a first spatialperiod λ₁ (also referred to herein as λ_(y)) over a stage-y directionwidth of the first magnet array 12. In some embodiments, the stage-ydirection width of the first magnet array 12 is generally equal to λ₁,so that the first magnetization directions of the first magnetizationsegments 14 exhibit a single first spatial period λ₁ over the stage-ydirection width of the first magnet array 12. In some embodiments, thefirst magnetization directions of the first magnetization segments 14exhibit multiple (e.g. an integer number of) first spatial periods λ₁which repeat over the stage-y direction width of the first magnet array12.

Similar to the first magnet array 12, the second magnet array 12 maycomprise a plurality of linearly elongated second magnetization segments14. However, the second magnetization segments 14 may be linearlyelongated in the stage-y direction (e.g. non-parallel to the stage-xdirection in some embodiments or generally orthogonal to the stage-xdirection in some embodiments). Each second magnetization segment 14 hasa corresponding second magnetization direction that is generallyorthogonal to the stage-y direction and at least two of the secondmagnetization segments 14 have second magnetization directions that aredifferent from one another. The second magnetization directions of thesecond magnetization segments 14 may exhibit a second spatial period λ₂(also referred to herein as λ_(x)) over a stage-x direction width of thesecond magnet array 12. In some embodiments, the stage-x direction widthof the second magnet array 12 is generally equal to λ₂, so that thesecond magnetization directions of the second magnetization segments 14exhibit a single second spatial period λ₂ over the stage-x directionwidth. In other embodiments, the second magnetization directions of thesecond magnetization segments 14 exhibit multiple second spatial periodsλ₂ which repeat over the stage-x direction width. In some embodiments,the first spatial period λ₁=λ_(y) is equal to the second spatial periodλ₂=λ_(x) and they may both be referred to as the spatial period λ.

Similar to the first magnet array 12, the third magnet array 12 maycomprise a plurality of third magnetization segments 14 linearlyelongated in the stage-x direction, where each third magnetizationsegment 14 has a corresponding third magnetization direction that isgenerally orthogonal to the stage-x direction and at least two of thethird magnetization segments 14 have third magnetization directions thatare different from one another. The third magnetization directions ofthe third magnetization segments 14 may exhibit the first spatial periodλ₁=λ_(y) (or a unique third spatial period λ₃) over a stage-y directionwidth of the third magnet array 12. In some embodiments, the stage-ydirection width of the third magnet array 12 is generally equal to λ₁(or λ₃), so that the third magnetization directions of the thirdmagnetization segments 14 exhibit a single first spatial period λ₁ (orsingle third spatial period λ₃) over the stage-y direction width. Inother embodiments, the third magnetization directions of the thirdmagnetization segments 14 exhibit multiple first spatial periods λ₁ (ormultiple third spatial periods λ₃) which repeat over the stage-ydirection width.

Similar to the second magnet array 12, the fourth magnet array 12 maycomprise a plurality of fourth magnetization segments 14 linearlyelongated in the stage-y direction, where each fourth magnetizationsegment 14 has a corresponding fourth magnetization direction that isgenerally orthogonal to the stage-y direction and at least two of thefourth magnetization segments 14 have fourth magnetization directionsthat are different from one another. The fourth magnetization directionsof the fourth magnetization segments 14 may exhibit the second spatialperiod λ₂=λ_(x) (or a unique fourth spatial period λ₄) over a stage-xdirection width of the fourth magnet array 12. In some embodiments, thestage-x direction width of the fourth magnet array 12 is generally equalto λ₂ (or λ₄), so that the fourth magnetization directions of the fourthmagnetization segments 14 exhibit a single second spatial period λ₂ (orsingle fourth spatial period λ₄) over the stage-x direction width. Inother embodiments, the fourth magnetization directions of the fourthmagnetization segments 14 exhibit multiple second spatial periods λ₂ (ormultiple fourth spatial periods λ₄) which repeat over the stage-xdirection width.

FIGS. 3A and 3B respectively depict partial schematic top views ofmoveable stages 110A, 110B incorporating magnet array assemblies 116A,116B according to particular embodiments which may be used as magnetarray assemblies 16 of moveable stage 10 (or any other moveable stagesdescribed herein) according to particular embodiments. Each of magnetarray assemblies 116A, 116B comprises a plurality of elongated segmentmagnet arrays 112. In the illustrated embodiment, each of magnet arrayassemblies 116A, 116B comprise four elongated segment magnet arrays112A, 112B, 112C, 112D (collectively, magnet arrays 112) which include afirst magnet array 112A comprising magnetization segments 114A elongatedin the stage-x direction, second magnet array 112B comprisingmagnetization segments 114B elongated in the stage-y direction, thirdmagnet array 112C comprising magnetization segments 114C elongated inthe stage-x direction and fourth magnet array 112D comprisingmagnetization segments 114D elongated in the stage-y direction. Becauseof their elongation directions, first and third magnet arrays 112A, 112Cmay be referred to as x-magnet arrays and their correspondingmagnetization segments 114A, 114C may be referred to herein asx-magnetization segments and second and fourth magnet arrays 112B, 112Dmay be referred to as y-magnet arrays and their correspondingmagnetization segments 114B, 114D may be referred to herein asy-magnetization segments. Other than for their locations and/ororientations, any of magnet arrays 112 in any one of magnet arrayassemblies 116A, 116B and/or in any one of moveable stages 110A, 110Bmay be substantially similar to one another. In this way, magnet arrayassemblies 116A, 116B and moveable stages 110A, 110B may be 90°rotationally symmetric about a stage-z oriented axis located at thestage-x-stage-y center of magnet array assemblies 116A, 116B and/ormoveable stages 110A, 110B.

Although their individual magnet arrays 112 may be similar to oneanother, magnet array assemblies 116A, 116B and moveable stages 110A,110B of the FIG. 3A and 3B embodiments have layouts which are similar toone another in some respects and differ from one another in otherrespects. In the case of both magnet array assemblies 116A, 116B, astage-x oriented edge of first magnet array 112A abuts against a stage-xoriented edge of second magnet array 112B (at abutment 155A), a stage-yoriented edge of the first magnet array 112A abuts against a stage-yoriented edge of the fourth magnet array 112D (at abutment 155B), astage-x oriented edge of third magnet array 112C abuts against a stage-xoriented edge of the fourth magnet array 112D (at abutment 155C), and astage-y oriented edge of the third magnet array 112C abuts against astage-y oriented edge of the second magnet array 112B (at abutment155D). Further, in the case of both magnet array assemblies 116A, 116B,the peripheral edges of magnet arrays 112 are aligned with one anotherto provide magnet array assemblies 116A, 116B with a generallyrectangular peripheral shape (from the top plan view). In particular,the stage-y oriented peripheral edges of first and second magnet arrays112A, 112B and the stage-y oriented peripheral edges of third and fourthmagnet arrays 112C, 112D are aligned with one another in the stage-ydirection. Further, the stage-x oriented peripheral edges of the firstand fourth magnet arrays 112A, 112D and the stage-x oriented peripheraledges of second and third magnet arrays 112B, 112C are aligned with oneanother in the stage-x direction.

In some embodiments, these abutments and/or peripheral edge alignmentsare not necessary and magnet array assemblies 16 may comprise as few asone elongated segment magnet array 12 or a plurality of elongatedsegment magnet arrays 12 which are spaced apart from one another (i.e.non-abutting), which have non-aligned peripheral edges and/or which abutone another with different abutment and/or alignment relationships. Forexample, in some embodiments, the stage-y oriented peripheral edges offirst and second magnet arrays 112A, 112B and the stage-y orientedperipheral edges of third and fourth magnet arrays 112C, 112D are notaligned with one another in the stage-y direction; and in someembodiments, the stage-x oriented peripheral edges of the first andfourth magnet arrays 112A, 112D and the stage-x oriented peripheraledges of second and third magnet arrays 112B, 112C are not aligned withone another in the stage-x direction.

The layout of magnet array assembly 116B differs from the layout ofmagnet array assembly 116A in that, for magnet array assembly 116B:corresponding stage-y oriented edges 157A, 157C of first and thirdmagnet arrays 112A, 112C are offset from one another in the stage-xdirection (by an offset Ox) and adjacent stage-x oriented edges 159A,159C of first and third magnet arrays 112A, 112C are spaced apart fromone another in the stage-y direction (by a first space Sy); andcorresponding stage-x oriented edges 157B, 157D of second and fourthmagnet arrays 112B, 112D are offset from one another in the stage-ydirection (by an offset Oy) and adjacent stage-y oriented edges 159B,159D of second and fourth magnet arrays 112B, 112D are spaced apart fromone another in the stage-x direction (by a second space Sx). It can beseen from FIG. 3B, that for magnet array assembly 116B, the stage-xdimensions of the first and third magnet arrays 112A, 112C are largerthan their corresponding stage-y dimensions, while the stage-ydimensions of the second and fourth magnet arrays 112B, 112D are largerthan their corresponding stage-x dimensions. These offsets Ox, Oy andspaces Sx, Sy give rise to a non-magnetized space 151 (with dimensionsSx by Sy) in the center of magnet arrays assembly 116B. The layout ofmagnet array assembly 116B may be advantageous (relative to the layoutof magnet array assembly 116A) because active coil traces interactingclosely with magnet array 112A may generate relatively little couplingforce on the magnet array 112C, and vice versa in magnet array assembly116B as compared to magnet array assembly 116A; and active coil tracesinteracting closely with magnet array 112B generate little couplingforce on the magnet array 112D, and vice versa in magnet array assembly116B as compared to magnet array assembly 116A.

The layout of magnet array assembly 116A differs from the layout ofmagnet array assembly 116B in that, for magnet array assembly 116A: thestage-x oriented edges of the first and second magnet arrays 112A, 112B(i.e. the stage-x oriented edges that provide abutment 155A) have thesame stage-x dimension; the stage-y-oriented edges of the first andfourth magnet arrays 112A, 112D (i.e. the stage-y oriented edges thatprovide abutment 155B) have the same stage-y dimension; the stage-xoriented edges of the third and fourth magnet arrays 112C, 112D (i.e.the stage-x oriented edges that provide abutment 155C) have the samestage-x dimension; and the stage-y-oriented edges of the second andthird magnet arrays 112B, 112C (i.e. the stage-y oriented edges thatprovide abutment 155D) have the same stage-y dimension. Further, withthese dimensions (and the above-described abutment and peripheral edgealignment features) magnet array assembly 116A does not have a spacethat is analogous to space 151 of magnet array assembly 116B. The layoutof magnet array assembly 116A may be advantageous (relative to thelayout of magnet array 116B) because the magnet array assembly footprint(in the stage-x and stage-y directions) is fully utilized for magneticfield generation.

Another difference between magnet array assemblies 116A, 116B is thatfor magnet array assembly 116A, the magnet array 112A that is furthestin the positive stage-x direction and furthest in the positive stage-ydirection comprises magnetization segments 114A which are elongated inthe stage-x direction and the other magnet arrays 112B, 112C, 112Dalternate between having magnetization segments 114B, 114C, 114Delongated in the stage-y and stage-x directions. In contrast, for magnetarray assembly 116B, the magnet array 112D that is furthest in thepositive stage-x direction and furthest in the positive stage-ydirection comprises magnetization segments 114D which are elongated inthe stage-y direction and the other magnet arrays 112A, 112B, 112Calternate between having magnetization segments 114A, 114B, 114Celongated in the stage-x and stage-y directions. In this description:magnet array assemblies, like magnet array assembly 116A of FIG. 3A,which have a magnet array that is furthest in the positive stage-xdirection and furthest in the positive stage-y direction and whichcomprises magnetization segments which are elongated in the stage-xdirection may be referred to as right-handed magnet array assemblies;and magnet array assemblies, like magnet array assembly 116B of FIG. 3B,which have a magnet array that is furthest in the positive stage-xdirection and furthest in the positive stage-y direction and whichcomprises magnetization segments which are elongated in the stage-ydirection may be referred to as left-handed magnet array assemblies. Itshould be understood that many variations to magnet array assemblies116A, 116B can be used in moveable stages 110A, 110B. In one example,magnet array assembly 116A of FIG. 3A can be changed from a right-handedto a left-handed variation. In another example, magnet array assembly116B of FIG. 3B can be changed from a left handed to a right handledvariation.

As discussed above, other than for their orientations, the magnet arrays112 in magnet array assemblies 116A, 116B and moveable stages 110A, 110Bmay be substantially similar to one another. However, the magnet arrays112 in magnet array assemblies 116A, 116B may have a wide variety ofpatterns of magnetization segments 114 (and their correspondingmagnetization directions). FIG. 3C is a cross-sectional view of anexemplary y-magnet array 112 (e.g. array 112B) which may be used in theFIG. 3A magnet array assembly 116A and/or in the FIG. 3B magnet arrayassembly 116B and/or in any of the other elongated segment magnet arrayassemblies described herein. Various other elongated segment magnetarrays 112 could be used in the FIG. 3A magnet array assembly 116Aand/or in the FIG. 3B magnet array assembly 116B and/or in any of theother elongated segment magnet array assemblies described herein. Forexample, Patent Cooperation Treaty Patent application Nos.PCT/CA2012/050751, PCT/CA2014/050739 and PCT/CA2015/050157 (all of whichare hereby incorporated by reference herein) disclose a number ofdifferent embodiments of elongated segment magnet arrays, each of whichcould be used for magnet arrays 112 in any of the elongated magnet arrayassemblies described herein (e.g. magnet arrays assemblies 116A, 116B).

In the illustrated cross-sectional view of FIG. 3C, magnet array 112comprises a plurality of magnetization segments 114, each of which has acorresponding magnetization direction (where the magnetizationdirections of magnetization segments 114 are indicated by arrows). Whilethe magnet array 112 of FIG. 3C is a y-magnet array, it will beappreciated that x-magnet arrays may be provided by merely altering theorientations of the illustrated magnet arrays and that the descriptionof magnet arrays 112 described herein should be understood to apply toy-magnet arrays 112 or x-magnet arrays 112 with adjustment oforientation, as appropriate. As can be seen from FIG. 3C, the stage-xdirection width of each magnetic segment 114 is generally equal to oneof

$\frac{\lambda_{x}}{4}\mspace{14mu} {or}\mspace{14mu} {\frac{\lambda_{x}}{8}.}$

In the case of the FIGS. 3A and 3B embodiments, the edge magnetizationsegments 114′ (i.e. magnetization segments 114′ at the edges of arrays112) have stage-x direction widths

$\left( \frac{\lambda_{x}}{8} \right)$

that are half of the stage-x direction widths

$\left( \frac{\lambda_{x}}{4} \right)\mspace{14mu}$

of the other (interior) magnetization segments 114. In some embodiments,the stage-x direction widths of each magnetic segment 114 may begenerally equal to one of

${\frac{\lambda_{x}}{N}\mspace{14mu} {or}\mspace{14mu} \frac{\lambda_{x}}{2\; N}},$

where N is any positive integer. In some embodiments, edge magnetizationsegments 114′ may have stage-x direction widths

$\left( \frac{\lambda_{x}}{2N} \right)$

that are half of the stage-x direction widths

$\left( \frac{\lambda_{x}}{N} \right)$

of the other (interior) magnetization segments 114. In some embodiments,N=N_(t) (where N_(t) represents the number of different magnetizationdirections in an array 112), as is the case in the illustratedembodiments of FIG. 3C. In the illustrated embodiments of FIG. 3C, theedge magnetization segments 114′ have magnetization directions that areoriented in the stage-z direction (in the positive stage-z direction inthe case of the illustrated embodiment). For any of the embodiments ofmagnet arrays 112 shown and/or described herein, the stage-z directionsof the magnetization segments 114 may be inverted from those shownand/or described herein.

The various magnet arrays 112 shown in the illustrated embodiments ofFIGS. 3A-3C exhibit a number of similar properties. The magnetizationdirections of magnetization segments 114 are orthogonal to theelongation directions of magnetization segments 114. At least two ofmagnetization segments 114 of each magnet array 112 are different fromone another. In general, magnet arrays 112 may comprise magnetizationsegments 114 with any suitable integer number N_(t) (N_(t)≥2) ofmagnetization directions. In the illustrated embodiment of FIG. 3C,N_(t)=4. The magnetization directions of magnetization segments 114exhibit a spatial period λ_(x) over the stage-x width of magnet arrays112. To avoid complicating the illustration of FIG. 3C, the spatialperiod λ_(x) is shown as λ without loss of generality. In the FIG. 3Cembodiment, the stage-x direction width (W_(mx)) of magnet array 112 isgenerally equal to λ_(x), so that the magnetization directions ofmagnetization segments 114 exhibit a single spatial period λ_(x) overthe stage-x direction width W_(mx) of magnet array 112. In someembodiments, the magnetization directions of first magnetizationsegments 114 may exhibit any positive integer number N_(m) spatialperiods λ_(x) which repeat over the stage-x direction width((W_(mx)=N_(m)λ_(x)) of magnet array 112. In the illustrated embodimentof FIG. 3C, the magnetization directions of magnetization segments 114are mirror symmetric relative to a plane of symmetry (extending in thestage-y and stage z-directions and passing through the stage-x directioncenter of magnet array 112 indicated by lines 141 shown in FIG. 3C).

Moveable stage 10 of displacement device 50 may comprise optionalbumpers (not shown) which may protect moveable stage 10 from othermoveable stages and other objects that may be introduced onto stator 30or into working region 36. Bumpers may be made of non-magnetic materialsto protect moveable stage 10 and its magnet array assembly 16. Furtherbumpers may prevent two or more moveable stages 10 from getting tooclose to one another (e.g. to a vicinity where their respectivemagnetization segments 14 might attract one another and mightundesirably influence the forces caused by current controllably driveninto coil traces 32, 34). Bumpers may also serve to prevent otherobjects with high magnetic permeability from getting too close to magnetarray assembly 16. For example, in the absence of non-magnetic bumpers,an iron or steel washer/screw/nuts dropped onto working region 36 can beattached to magnet array assembly 16 and cause system failure. Examplesof suitable bumpers which can be used for any of the moveable stagesdescribed herein are described in PCT/CA2015/050157.

In some embodiments, moveable stage 10 may comprise a stage supportstructure which may be fabricated from highly magnetically permeablematerial (e.g. with relative magnetic permeability greater than 100),such as iron, ferrite, cobalt, combinations of these materials and/orthe like. High magnetic permeability helps enhance the magnetic fieldbelow (e.g. in the negative stator-z direction relative to) magnet arrayassembly 16, which is where the coil traces of stator 30 are typicallylocated during operation. In some embodiments, it may be beneficial touse a stage support structure without back iron. Such embodiments may bedesirable to minimize the weight of moveable stage 10, for example. Suchstage support structures can be fabricated from aluminum, ceramic,carbon-fiber reinforced composite materials, combinations of thesematerials and/or the like. Reducing the weight of stage support layermay help to minimize moveable stage inertia.

Stator

Various embodiments and additional detail of stator 30 are now provided.Referring back to FIG. 1 described above, stator 30 comprises a statorcoil assembly 35 which comprises at least the traces of a plurality ofelectrically conductive coils 31. Coils 31 are shaped to provide firstand second pluralities of coil traces 32, 34 which are respectivelyelongated in non-parallel directions. In particular embodiments, such asdepicted in FIG. 1A, first plurality of coil traces 32 is orthogonal tosecond plurality of coil traces 34. In particular embodiments, such asdepicted in FIG. 1A, first plurality of coil traces 32 is distributedover at least a portion of a first layer 40 and generally elongated in astator-x direction; and second plurality of coil traces 34 isdistributed over at least a portion of a second layer 42 and generallyelongated in a stator-y direction. In some embodiments, such as depictedin FIG. 1A, the first and second layers 40, 42 over which first andsecond pluralities of coil traces 32, 34 are respectively distributedmay be located at different (e.g. first and second) stator-z locationsand layers 40, 42 may overlap one another in the stator-z direction,although this is not necessary. In some embodiments, first and secondlayers 40, 42 may be provided in different excitation regions (alsoreferred to herein as stator tiles or tiles and described in more detailbelow), but at the same stator-z location.

In some embodiments, stator 30 may comprise additional pluralities ofcoil traces (not shown) which may be distributed over portions ofadditional layers at corresponding additional stator-z directionlocations. For example, stator 30 may comprise a first additionalplurality of coil traces (not shown) distributed over at least a portionof a first additional layer at a corresponding first additional stator-zlocation and generally elongated in a stator-x direction; and a secondadditional plurality of coil traces (not shown) distributed over atleast a portion of a second additional layer at a corresponding secondadditional stator-z location and generally elongated in a stator-ydirection. Additional pluralities of coil traces are not limited tobeing elongated in the stator-x or stator-y directions. In someembodiments, additional pluralities of coil traces are provided whichare generally elongated in angular directions between the stator-x andstator-y directions. For example, in some embodiments, stator 30 maycomprise one or both of: a first additional angular plurality of coiltraces (not shown) distributed over at least a portion of a firstadditional angular layer at a corresponding first additional angularstator-z location and generally elongated in a direction split betweenthe positive stator-x and positive stator-y directions (e.g. at 45°counter-clockwise around a stator-z axis from the positive stator-xdirection in some embodiments); and a second additional angularplurality of coil traces (not shown) distributed over at least a portionof a second additional angular layer at a corresponding secondadditional angular stator-z location and generally elongated in adirection split between the negative stator-x and positive stator-ydirections (e.g. at 45° clockwise around a stator-z axis from thenegative stator-x direction in some embodiments). In other embodiments,additional pluralities of coil traces may be elongated at angles a otherthan 45° from the stator-x and/or stator-y directions. Such coil tracesmay be referred to herein as α-oriented coil traces or α-traces, where αis their angle as measured from one of the stator-x or stator-y axes.

In some embodiments, coil traces 32, 34 in layers 40, 42 at differentstator-z locations may overlap one another in the stator-z direction.The two dimensional space over which coil traces 32, 34 overlap oneanother in the stator-z direction may define a working region 36 overwhich moveable stage 10 is moveable relative to stator 30. In someembodiments, coil traces 32, 34 in each corresponding layer 40, 42 maybe distributed throughout their respective layers 40, 42, so that coiltraces 32, 34 and/or layers 40, 42 may overlap in the stator-z directionat all locations in working region 36. This is not necessary. In someembodiments, coil traces 32, 34 may occupy particular excitation regions(also referred to as stator tiles and described in more detail below)that occupy less than an entirety of a corresponding layer 40, 42. Someof coil traces 32, 34 may be connected at their ends to form atwo-phase, three-phase, or multiple-phase winding configuration asdescribed in more detail below. While working region 36 is atwo-dimensional space, this description may describe working region 36as a feature of stator 30, for convenience.

FIG. 4 shows a displacement device 150 according to a particularembodiment of the invention. FIG. 4 comprises a moveable stage 110similar to one of those shown in FIGS. 3A-3C and a stator 130. Stator130 of the FIG. 4 embodiment comprises an optional stator bearing layer145, stator coil assembly 135, coil supporting layer 137, powerelectronics layer 138, and optional cooling layer 139. Stator coilassembly 135 may comprise the aforementioned coils 31 and/or coil traces32, 34.

Optional stator bearing layer 145 may overlap with stator coil assembly135 in stator-z direction over the stator-x/stator-y span of workingregion 36 (not shown in FIG. 4). Stator bearing layer 145 may comprise agenerally planar stator bearing surface 126 which may bear against (orbe separated by an air gap from) stage bearing surface 124 of stagebearing layer 118 of moveable stage 110. In the illustrated embodiment,stage bearing surface 124 faces the negative stator-z direction andstator bearing surface 126 faces the positive stator-z direction.Various stator bearing layers and restrictor layers are described inPatent Cooperation Treaty application No. PCT/CA2015/050157 and may beused with any of the embodiments of stator 30 (or 130, 230 etc.) asdescribed herein.

Coil supporting layer 137 may provide mechanical support to stator coilassembly 135. Stator coil assembly 135 of the FIG. 3 embodiment may besubstantially similar to stator coil assembly 35 of the FIG. 1embodiment and may comprise coils 31 shaped to provide coil traces 32,34 (and any additional coil traces) having features similar to those ofthe FIG. 1 embodiment. Controller 60 may be connected to deliver controlsignals to one or more amplifiers 70 and controller 60 may be configuredto use those control signals to control the currents driven byamplifier(s) 70 into at least some of coil traces 32, 34 to therebycause moveable stage 10, 110 to track a desired position within workingregion 36—e.g. a desired position, (x_(r), y_(r)), within working region36, where x_(r) is a desired position of moveable stage 10, 110 in thestator-x direction and y_(r) is a desired position of moveable stage 10,110 in the stator-y direction.

In some embodiments, when in operation, moveable stage bearing surface124 is in close proximity with (e.g. adjacent to) and generally parallelto stator bearing surface 126. In some embodiments, the stator-zdirection gap between moveable stage 110 and stator 130 is less than 10mm, and is typically around 1 mm. This space between stator 130 andmoveable stage 110 can be maintained (at least in part) by Z-directionforces created by the interaction of the magnetic fields generated bycurrent in coil traces 32, 34 of stator 130 with magnet arrays 112 ofmoveable stage 110 as discussed below. In some embodiments, this space(or air gap) between stator 130 and moveable stage 110 can be maintainedusing additional lifting and/or hoisting magnets, aerostatic bearings,roller bearings and/or the like (not shown), as is known in the art. Insome embodiments, as discussed above, the magnetic forces generated bythe interaction of currents driven into coil traces 32, 34 and magnetarray(s) 112 of moveable stage 110 may be controlled (e.g. by controller60), such that moveable stage 110 is attracted toward stator 130whenever the currents are being controllably driven into coil traces 32,34.

FIG. 5 shows a schematic top view of a stator coil assembly 35 accordingto a particular embodiment which may be used in displacement device 50(FIG. 1), displacement device 150 (FIG. 4) or any of the otherdisplacement devices described herein. Stator coil assembly 35, asdepicted, comprises a plurality of excitation regions 43A-43I(collectively, excitation regions 43). Excitation regions 43 may also bereferred to herein as stator tiles 43 or, for brevity, tiles 43. In someembodiments, each of excitation regions 43 is rectangular in shape. Insome embodiments, excitation regions 43 may have other shapes (e.g.triangular, hexagonal and/or the like). Each location in each ofexcitation regions 43 may overlap corresponding coil trace layers 40, 42at different stator-z locations and corresponding coil traces 32, 34(and any additional layers and additional coil traces) in the stator-zdirection. Coil traces 32, 34 that overlap a particular one ofexcitation regions 43 in the stator-z direction may be said to be coiltraces 32, 34 in, of, associated with or corresponding to the particularone of excitation regions 43. Each coil trace 32, 34 in each excitationregion 43 can be excited with a controllable current, where such currentmay be controlled by controller 60 which may use control signals tocontrol amplifier(s) 70 which in turn drive current into coil traces 32,34. Each of excitation regions 43 may be connected to a correspondingamplifier module, which may be located in power electronics layer 138(see FIG. 4) or may be spatially separated from stator 30 and connectedto coil traces 32, 34 in its excitation region 43 using suitableelectrical connections. Currents driven into the coil traces 32, 34 ineach excitation region 43 can be independently controlled. In someembodiments, two or more excitation regions 43 may share a commonamplifier 70 by connecting their corresponding coil traces in parallelor serially. It is not necessary that a particular stator coil assembly35 comprise a plurality of excitation regions. In some embodiments, itis sufficient for a stator coil assembly 35 to have a single excitationregion that spans the entire working region.

FIGS. 6A-6C each show schematic depictions of portions of coil tracelayers 40, 42 and/or coil traces 32, 34 in a corresponding excitationregion 43. FIG. 6A is a cross-sectional view (along a stator-x/stator-zplane) of one excitation region 43 of stator coil assembly 35 comprisinga plurality of coil trace layers 40A, 40B, 42A, 42B (collectively, coiltrace layers, 40, 42). In the FIG. 6A embodiment, each coil trace layer40, 42 extends in the stator-x and stator-y directions acrosscorresponding excitation region 43, although this is not necessary. Inthe FIG. 6A embodiment, stator 30 comprises a plurality of x-tracelayers 40A, 40B located at different stator-z locations and a pluralityof y-trace layers 42A, 42B located at different stator-z locations inone excitation region 43 (although this is not necessary). In the FIG.6A embodiment, each coil trace layer 40, 42 is separated from adjacentcoil trace layers 42, 40 by an insulation layer 47. Insulation layer 47prevents electrical conduction between coil trace layers 40, 42. Eachcoil trace layer 40, 42 extends generally in the stator-x and stator-ydirections with its normal direction generally parallel to the stator-zdirection. As discussed above, each coil trace layer 40, 42 comprises aplurality of coil traces which may be distributed over at least aportion of the layer and which extend in a particular stator direction(e.g. in the stator-x direction or the stator-y direction).

FIG. 6B is a schematic cross-sectional view (along a stator-x/stator-yplane) of a portion of a first coil trace layer 40A according to aparticular embodiment. Coil trace layer 40B may have characteristicssimilar to coil trace layer 40A. The portion of coil trace layer 40Ashown in the FIG. 6B embodiment comprises a plurality (referred toherein as a group) 66 of coil traces 32A, 32B, 32C, 32A′, 32B′, 32C′(collectively, coil traces 32), with each coil trace 32 linearlyelongated in the stator-x direction. Due to their elongation in thestator-x direction, coil traces 32 may be referred to herein as x-traces32 and group 66 and coil trace layer 40A may be respective referred toas an x-trace group 66 and an x-trace layer 40 or an x-group 66 and anx-layer 40. The x-traces 32 may extend in the stator-x direction acrossx-trace layer 40 and/or across a corresponding excitation region 43. Thex-trace layer 40 in one excitation region 43 may comprise one or morex-trace groups 66, which may be distributed across x-trace layer 40and/or a corresponding excitation region 43 in the stator-y direction.As explained in more detail below, in some embodiments, each x-tracegroup 66 may comprise a plurality of x-coil traces 32 which may bedriven (by one or more connected amplifiers 70) with correspondingmulti-phase currents so that one phase of the multi-phase currents isdriven into each x-coil trace 32 in the x-trace group 66. In someembodiments, the multi-phase currents have a number n of effectivephases and the number of x-traces 32 in each x-trace group 66 is 2n,where each x-trace 32 is connected to receive a phase of the multiphasecurrent in one direction or in the opposing direction. FIG. 6C is aschematic cross-sectional view (along a stator-x/stator-y plane) of asecond coil trace layer 42A according to a particular embodiment. Coiltrace layer 42B may have characteristics similar to coil trace layer42A. Coil trace layer 42A of the FIG. 6C embodiment comprises aplurality (referred to herein as a group) 68 of coil traces 34A, 34B,34C, 34A′, 34B′, 34C′ (collectively, coil traces 34), with each coiltrace 34 linearly elongated in the stator-y direction. Due to theirelongation in the stator-y direction, coil traces 34 may be referred toherein as y-traces 34 and group 68 and coil trace layer 42A may berespective referred to as a y-trace group 68 and a y-trace layer 42 or ay-group 68 and a y-layer 42. The y-traces 34 may extend in the stator-ydirection across y-trace layer 42 and/or a corresponding excitationregion 43. The y-trace layer 42 in one excitation region 43 may compriseone or more y-trace groups 68, which may be distributed across y-tracelayer 42 and/or a corresponding excitation region 43 in the stator-xdirection. As explained in more detail below, in some embodiments, eachy-trace group 68 may comprise a plurality of y-coil traces 34 which maybe driven (by one or more connected amplifiers 70) with correspondingmulti-phase currents so that one phase of the multi-phase currents isdriven into each y-coil trace 34 in the y-trace group 68. In someembodiments, the multi-phase currents have a number n of effectivephases and the number of y-traces 34 in each y-trace group 68 is 2n,where each y-trace 34 is connected to receive a phase of the multiphasecurrent in one direction or in the opposing direction.

It will be appreciated that the number of coil traces 32, 34 in groups66 need not be limited to the exemplary six traces shown in FIGS. 6B, 6Calthough this number of traces in a group is convenient for usingthree-phase current as explained in more detail below. In someembodiments, coil trace layers 40, 42 adjacent to one another in thestator-z direction may comprise coil traces that are non-parallel withrespect to one another. In some embodiments, coil trace layers 40, 42adjacent to one another in the stator-z direction may comprise coiltraces that are orthogonally oriented with respect to one another. Itwill be appreciated that the number of coil trace layers 40, 42 instator 30 need not be limited to the four traces shown in theillustrative embodiment of FIG. 6A. In general, stator 30 may compriseany suitable number of coil trace layers 40, 42. Further, it is not arequirement that the orientations of coil traces in coil trace layers40, 42 adjacent to one another in the stator-z direction be differentfrom one another. In some embodiment, coil traces may be provided whichextend in directions other than the stator-x or stator-y directions.Such traces which may be referred to as a-traces are described inPCT/CA2015/050157.

Further details of stator, coil traces, excitation regions and coiltrace layers are described in Patent Cooperation Treaty Patentapplication Nos. PCT/CA2012/050751, PCT/CA2014/050739 andPCT/CA2015/050157.

Control and Operation

In some embodiments, x-traces 32 in different x-trace layers 40, indifferent x-trace groups 66 and/or individual x-traces 32 may each beindependently driven (by amplifiers 70 under the control of controller60) with different power amplifier channels. Similarly, in someembodiments, y-traces 34 in different y-trace layers 42, in differenty-trace groups 68 and/or individual y-traces 34 may each beindependently driven (by amplifiers 70 under the control of controller60) with different power amplifier channels. While such independentconnection provides maximum flexibility of control, this configurationis not necessary in all embodiments or applications. In someembodiments, x-traces 32 in different x-trace layers 40 or in differentx-trace groups 66 of one excitation region 43 may be connected seriallyor in parallel and y-traces 34 in different y-trace layers 42 or indifferent y-trace groups 68 of one excitation region 43 may be connectedserially or in parallel.

In general, current driven through the coil traces 32, 34 is used topropel moveable stage 10 to a desired position relative to stator 30(e.g. in working region 36) and/or to a desired orientation relative tostator 30. Current driven in x-traces 32 may be used to impart forceonto (and thereby propel) moveable stage 10 along a stator-y directionto track a desired stator-y position y_(r); current driven in y-coiltraces 34 may be used to impart force onto (and thereby propel) moveablestage 10 along a stator-x direction to track a desired stator-x positionx_(r). Either or both of current driven in x-traces 32 and y-traces 34may be used to pivot moveable stage 10 around a stator-z oriented axis.Either or both of current driven in x-traces 32 and y-traces 34 may beused to impart force onto (and thereby propel) moveable stage 10 in astator-z direction. Current driven in x-traces 32 may be used to pivotmoveable stage 10 around a stator-x orientied axis; current driven iny-traces 34 may be used to pivot moveable stage 10 around a stator-yoriented axis. The schematic illustration of displacement device 50shown in FIG. 7 is useful for explaining the particulars of theoperation of displacement device 50. The FIG. 7 displacement device 50comprises a moveable stage 10 and a magnet array assembly 16 which aresimilar to moveable stage 110 and magnet array assembly 116B shown inFIG. 3B, although the principles of operation are similar for othermoveable stages and other magnet array assemblies 16 described herein. Aportion of stator 30 (e.g. an excitation region 43 or a portion of anexcitation region 43) is shown schematically in FIG. 7 by anintersecting array of lines which represent x-traces 32 and y-traces 34.To facilitate explanation, it is assumed that each x-trace 32 and eachy-trace 34 is independently controllable—i.e. that the current driveninto such traces 32, 34 is independently controllable. X-traces 32include two x-trace groups 66A, 66B which are shown with bold lines toindicate that they are active (i.e. that current is being driven intothe x-traces 32 of x-trace groups 66A, 66B) and y-traces 34 include twoy-trace groups 68A, 68B which are shown with bold lines to indicate thatthey are active (i.e. that current is being driven into the y-traces 34of y-trace groups 68A, 68B). The magnetic fields associated with thecurrents being driven in x-trace groups 66A, 66B interact primarily withx-magnet arrays 112A, 112C respectively; and the magnetic fieldsassociated with the currents being driven in y-trace groups 68A, 68Binteract primarily with y-magnet arrays 112B, 112D respectively. Moreparticularly: when x-traces 32 in x-trace group 66A are carryingcurrent, they interact with x-magnet array 112A to impart forces onmoveable stage 10 in the y and z directions; when y-traces 34 in y-tracegroup 68A are carrying current, they interact with y-magnet array 112Bto impart forces on moveable stage 10 in the x and z directions; whenx-traces 32 in x-trace group 66B are carrying current, they interactwith x-magnet array 112C to impart forces on moveable stage 10 in the yand z directions; and when y-traces 34 in y-trace group 68B are carryingcurrent, they interact with y-magnet array 112D to impart forces onmoveable stage 10 in the x and Z directions.

It will be appreciated that coil traces 32, 34 shown in FIG. 7 can beselectively activated (e.g. by driving current through the coil traces32, 34) to impart desired forces on moveable stage 10 and to therebycontrol the motion (e.g. position) of moveable stage 10 with six degreesof freedom relating to the rigid body motion of moveable stage 10. Insome embodiment, each x-trace group 66 and each y-trace group 68 can beselectively activated (e.g. by driving current through the tracescorresponding to the coil trace group 66, 68) or deactivated. When acoil trace group 66, 68 is selectively activated, the coil tracescorresponding to the coil trace group 66, 68 may be driven withmulti-phase currents by one or more multi-phase amplifiers 70. Ingeneral, such multi-phase currents can comprise two-phases,three-phases, or any suitable number of phases. When moveable stage 10is shown in the particular position shown in FIG. 7, coil traces 32, 34other than those in groups 66A, 66B, 68A, 68B may be inactive. However,it will be appreciated that as moveable stage 10 moves relative tostator 30, different groups of coil traces 32, 34 may be selected to beactive and to impart desired forces on moveable stage 10.

It may be observed that the active coil traces 32, 34 in groups 66A,66B, 68A, 68B appear to interact with other magnet arrays. For example,when carrying current, x-traces 32 in x-trace group 66B interact withx-magnet array 112C as discussed above, but x-traces 32 in x-trace group66B also pass under a portion of y-magnet array 112B. One might expectthat, the currents in x-trace group 66B might interact with the magnetsin y-magnet array 112B and impart additional forces on moveable stage10. However, because of the aforementioned characteristics of y-magnetarray 112B, the forces that might have been caused by the interaction ofcurrents in x-trace group 66B and the magnetization segments 114B ofy-magnet array 112B cancel one another out, such that these parasiticcoupling forces may be eliminated or kept to a minimal level. Moreparticularly, the characteristics of y-magnet array 112B that eliminateor reduce these cross-coupling forces include: y-magnet array 112Bcomprises magnetization segments 114B which are generally elongated inthe stage-y direction with varying magnetizations which are orientedorthogonally to the stage-y direction; the x-dimension width W _(mx) ofy-magnet array 112B is W _(mx) =N_(m)λ_(x) where N_(m) is an integer andλ_(x) is the magnetic period λ_(x) described above; and y-magnet array112B is mirror symmetric about a y-z plane 141 that runs through thecenter of the stage-x dimension of y-magnet array 112B. Similarcharacteristics of y-magnet array 112D may eliminate or minimizecross-coupling from x-traces 32 in x-trace group 66A. In an analogousmanner, the characteristics of x-magnet array 112A may eliminate orreduce cross-coupling forces from y-traces 34 in y-trace group 68A. Suchcharacteristics of x-magnet array 112A include: x-magnet array 112Aincludes magnetization segments 114A which are generally elongated inthe stage-x direction with varying magnetizations which are orientedorthogonally to the stage-x direction; the y-dimension width W_(my) ofx-magnet array 112A is W_(my)=N_(m)λ_(y) where N_(m) is an integer andλ_(y) is the magnetic period λ_(y) described above; and x-magnet array112A is mirror symmetric about a x-z plane that is orthogonal to they-axis and runs through the center of the y-dimension of x-magnet array112A. Similar characteristics of x-magnet array 112C may eliminate orminimize cross coupling from y-traces 34 in y-trace group 68B.

Further details relating to how currents driven into coil traces 32, 34impart forces onto moveable stage 10 are described in PCT/CA2012/050751.

Displacement device 50 comprises one or more amplifiers 70 which areconnected (e.g. with suitable electrical connections (not expresslyshown in FIG. 1)) to drive a plurality of currents into coil traces 32,34. Amplifiers 70 are controlled by controller 60 which is connected andconfigured to provide control currents to amplifiers 70. Controller 60(and components thereof) may comprise hardware, software, firmware orany combination thereof. For example, controller 60 may be implementedon a programmed computer system comprising one or more processors, userinput apparatus, displays and/or the like. Controller 60 may beimplemented as an embedded system with a suitable user interfacecomprising one or more processors, user input apparatus, displays and/orthe like. Processors may comprise microprocessors, digital signalprocessors, graphics processors, field programmable gate arrays, and/orthe like. Components of controller 60 may be combined or subdivided, andcomponents of controller 60 may comprise sub-components shared withother components of controller 60. Components of controller 60, may bephysically remote from one another. Controller 60 may be connected (e.g.with suitable electrical connections (not expressly shown in FIG. 1)) todeliver control signals to amplifiers 70. Controller 60 may beconfigured (e.g. using suitable software, logic configuration and/or thelike) to use those control signals to control the currents driven byamplifiers 70 into at least some of coil traces 32, 34 to thereby causemoveable stage 10 to track a desired position within relative to stator30 in working region 36—e.g. a desired position, (x_(r), y_(r)), withinworking region 36, where x_(r) is a desired position of moveable stage10 in the stator-x direction and y_(r) is a desired position of moveablestage 10 in the stator-y direction.

FIG. 8A shows a schematic block diagram of a control system 58 suitablefor use in controlling any of the displacement devices 50 describedherein according to a particular embodiment. Although they may bedescribed as different embodiments, except where otherwise specificallynoted, control system 58 and any of the control techniques, embodimentsand methods described in the remainder of this description may be usedwith any of the displacement devices 50 described herein. Control system58 of the FIG. 8A embodiment comprises controller 60, one or moreamplifiers 70 and stator coil assembly 35. Controller 60 may beconfigured to control (e.g. by providing control signals to) one or moreamplifiers 70 (illustrated, in FIG. 8A, as power amplifier 70) to drivecurrents into the plurality of coil traces in coil trace assembly 35.Such currents can be used by controller 60 to controllably move moveablestage 10 relative to stator 30 via forces associated with theinteraction between the magnetic fields generated by currents in theplurality of coil traces and the magnetic fields of the magnet arrayassembly 16 on moveable stage 10. The currents may be controlled bycontroller 60 such that these magnetic forces on moveable stage 10 mayattract moveable stage 10 toward stator 30 (e.g. in the negativestator-z direction) or may force stage 10 away from stator 30 (e.g. inthe positive stator-z direction) at all times when controller 60 iscontrolling the currents driven by the one or more amplifiers 70.

In the illustrated embodiment, controller 60 is shown as comprising atrajectory generator 62 which generates desired or reference positionsfor each moveable stage 10. Such reference positions may include any oneor more of: a desired or reference stator-x position x_(r) of moveablestage 10, a desired or reference stator-y position y_(r) of moveablestage 10, a desired or reference stator-z position z_(r) of moveablestage, a desired rotational orientations rz_(r) of moveable stage 10about a stage-z oriented axis (e.g. a stage-z oriented axis through thestage-x/stage-y center of moveables stage 10 or magnet array assembly16), a desired rotational orientations rx_(r) of moveable stage 10 abouta stage-x oriented axis (e.g. a stage-x oriented axis through thestage-y/stage-z center of moveables stage 10 or magnet array assembly16) and a desired rotational orientations ry_(r) of moveable stage 10about a stage-y oriented axis (e.g. a stage-y oriented axis through thestage-x/stage-z center of moveables stage 10 or magnet array assembly16). The reference positions (x_(r), y_(r), z_(r), rx_(r), ry_(r),rz_(r)) (or any subset thereof) generated by trajectory genereator 62are typically based on user requirements, application requirementsand/or feedback 63 relating to moveable stage(s) 10. By way ofnon-limiting example, feedback 63 may comprise measured characteristics,such as position, velocity, accelleration and/or orientation of moveablestage(s) 10 which may be obtained from suitable sensors. Feedback 63 canoriginate from any suitable measurement device(s), system(s) and/ormethod(s). Some non-limiting examples of suitable measurement device(s),system(s) and/or method(s) are described in Patent Cooperation Treatyapplication Nos. PCT/CA2012/050751 and PCT/CA2014/050739. For brevity,the remainder of this description will refer to controllably movingmoveable stage(s) 10 to reference positions (x_(r), y_(r)) without lossof generality that similar principles could be used to control themotion (e.g. position) of movable stage(10) with the six degrees offreedom corresponding to (x_(r), y_(r), z_(r), rx_(r), ry_(r), rz_(r)).In the illustrated embodiment, controller 60 also comprises a currentcommand generator 64. Typically, although not necessarily, the desiredposition (x_(r), y_(r)) of a moveable stage 10 will vary over time, suchthat each of the reference positions x_(r), y_(r) is a function of timeand may be described herein as x_(r)(t), y_(r)(t) at a particular time,t. The evolutions of the desired positions (x_(r), y_(r)) over time maybe referred to as a desired or reference trajectory. Generally, eachmoveable stage 10 has a unique reference trajectory. For brevity, exceptwhere otherwise dictated by the context or the description, thisdescription will focus on the trajectory and corresponding control ofone moveable stage 10, it being understood that trajectories and controlof other moveable stages 10 may be similarly implemented. Currentcommand generator 64 receives the desired position (x_(r), y_(r)) fromtrajectory generator 62 and feedback 63 and, based on this information,creates corresponding current control signals i_(r) using a suitablemotion control technique and a sutiable current commutation technique.Some examples of suitable motion control and current commutationtechniques are described Patent Cooperation Treaty application No.PCT/CA2012/050751. Current command generator 64 provides current controlsignals i_(r) to amplifier(s) 70. It will be appreciated that currentcontrol signals i_(r) may comprise a plurality of control signals. Inresponse to these current control signals i_(r), amplifier(s) 70 drivecurrents i_(x), i_(y) into at least some of the coil traces 32, 34 ofstator coil assembly 35. In some embodiments, first currents i_(x) mayrepresent the currents driven into a first plurality of coil traces(e.g. stator-x oriented coil traces 32) and second currents i_(y) mayrepresent the currents driven into a second plurality of coil traces(e.g. stator-y oriented coil traces 34). Accordingly, the currents i_(x)may be referred to herein as x-currents and the currents i_(y) may bereferred to herein as y-currents. As discussed above, stator coilassembly 35 may also comprise α-oriented coil traces and amplifier(s) 70may additionally or alternatively drive currents i_(α) into thesetraces. However, except where otherwise dictated by the context,discussion of drive currents i_(α) is omitted for brevity from thedescription of motion control.

FIG. 8B schematically depicts one possible connection scheme to connecta plurality (e.g. a y-trace group 68) of y-traces 34 in one coil tracelayer 42 within an excitation region 43 of stator 30 according to aparticular embodiment. It will be appreciated that a plurality (e.g. anx-trace group 66) of x-traces 32 in layer 40 within excitation region 43of stator 30 may have characteristics analogous to those of y-tracegroup 66 shown in FIG. 8B. While y-traces 34 shown in FIG. 8B aregenerally elongated in the stator-y direction, there may be someterminal connections near the edges of one excitation region 43 whichconnect different y-traces 34 together. Trace terminating connectionssometimes extend through one or more other layer(s) (e.g. another layerin the stator-z direction). The illustrated embodiment of FIG. 8Bdepicts a three-phase effective current embodiment where the y-currentsi_(y) corresponding to the y-traces 34 of y-trace group 68 comprisethree different current phases i_(jy) (j=0,1,2), each of which flowsalong a first y-trace 34A, 34B, 34C in a first direction and returnsalong a second y-trace 34A′, 34B′, 34C′ in an opposite, direction (e.g.current i_(0y) flows in one direction along y-trace 34A and flows in theopposite direction along y-trace 34A′). This current configuration maybe achieved by appropriate connection of amplifiers 70 to y-traces 34A,34B, 34C, 34A′, 34B′, 34C′ in a star configuration.

In the FIG. 8B embodiment, the currents i_(y) corresponding to they-traces 34 of y-trace group 68 may be described as comprising threeeffective current phases, because these currents i_(y) include threecurrent phases i_(jy) flowing in the first direction and returning inthe opposing direction at phases that are 180° out of electrical phasewith one another. For example, in FIG. 8B embodiment, the current intrace 34A has the same amplitude as the current in trace 34A′, but isflowing in an opposite direction; therefore, the currents in traces 34A,34A′ are not independent and are considered to be one effective currentphase. In some embodiments, the currents i_(y) corresponding to they-traces 34 of a y-trace goup 68 may comprie multi-phase currentscomprising a plurality m_(p) of current phases i_(jy)(j=0, 1, . . . ,m_(p)−1), where m_(p) is an integer greater than one. Similarly, thecurrents i_(x) corresponding to the x-traces 32 of an x-trace group 66may comprise multi-phase currents comprising a plurality n_(p) ofcurrent phases i_(kx) (k=0, 1, . . . , n_(p)−1), where n_(p) is aninteger greater than one. The currents i_(x) may be referred to as firstcurrents i_(x) or x-currents i_(x) and their corresponding currentphases i_(kx) may be referred to as first current phases i_(kx) orx-current phases i_(kx). The currents i_(y) may be referred to as secondcurrents i_(y) or y-currents i_(y) and their corresponding currentphases i_(jy) may be referred to as second current phases i_(jy) ory-current phases i_(jy). In some embodiments, the first currents i_(x)comprise a plurality of first current phases, i_(kx), where k is aninteger from 0 to n_(p)−1 representing a first phase index. Suchembodiments may be described has having n_(p) effective first currentphases i_(kx). Similarly, in some embodiments, the second currents i_(y)comprise a plurality of second current phases, i_(jy), where j is aninteger from 0 to m_(p)−1 representing a second phase index, where m_(p)is the effective number of second current phases.

To control the position of moveable stage 10 relative to stator 30 indisplacement device 50, it may be desirable to obtain feedback 63 whichmay comprise, for example, measured characteristics, such as position,velocity, accelleration and/or orientation of moveable stage(s) 10relative to stator 30 or to some other reference. Feedback 63 may beobtained from suitable sensors, measurement systems measurement methodsand/or the like. Any suitable sensors, measurement systems measurementmethods and/or the like may be used to determine feedback 63.Non-limiting examples of suitable sensors which may be used to providesome or all of feedback 63 include: laser displacement interferometers,two-dimensional optical encoders, laser triangulation sensors,capacitive displacement sensors, eddy current displacement sensors,reflective surfaces suitable for interferometry, accelerometers,Hall-effect sensors and/or the like. Different position sensingtechniques can be combined to provide an overall system. Varioussuitable feedback sensor systems and methods are described in PatentCooperation Treaty application Nos. PCT/CA2012/050751 andPCT/CA2014/050739.

FIG. 9 depicts and embodiment of displacement device 50 comprising afeedback sensing system 80 comprising a plurality of magnetic fieldsensors 82 distributed in an array 83 in a plane extending in thestator-x direction and the stator-y direction with a normal direction inthe stator z-direction. Sensors 80 may generate feedback 63 (see FIG.8A) which may be used by controller 60 to determine or estimate measuredcharacteristics of moveable stage 50. By way of non-limiting example,controller 60 may determine the position, velocity, acceleration and/ororientation of moveable stage 50 relative to stator 30, relative to somereference on or associated with stator 30 and/or relative to some otherreference (e.g. some other static reference). In some embodiments, array83 of sensors 82 is arranged in stator-x oriented sensor rows andstator-y oriented sensor columns, where sensors 82 in a stator-xoriented sensor row are generally aligned with one another in thestator-x direction and sensors 82 in a stator-y oriented sensor columnare generally aligned with one another in the stator-y direction.Magnetic field sensors may comprise hall-effect sensors,magneto-resistive sensing elements, magneto-strictive sensing elementsand/or any suitable sensor element that is sensitive to magnetic fieldflux density. Suitable sensing systems 82 incorporating sensor arrays 83which may be used to generate feedback 63 are described in detail inPatent Cooperation Treaty application No. PCT/CA2014/050739 and may beused with any of the displacement devices described herein.

Multiple Moveable Stages on Rectangular Stator Tiles

FIG. 10A shows a non-limiting embodiment of a moveable stage 210 and acorresponding magnet array assembly 216 according to a particularembodiment. Magnet array assembly 216 comprises a plurality (e.g. fourin the illustrated embodiment) of magnet arrays 212A, 212B, 212C, 212D(collectively, magnet arrays 212). For brevity, magnet arrays 212A,212B, 212C, 212D of the FIG. 10A magnet array assembly 216 may bereferred to as magnet arrays A, B, C, D. Magnet array assembly 216 is anelongated segment magnet array assembly 216 comprising a plurality ofelongated magnet arrays 212. Magnet array assembly 216 is similar tomagnet array assembly 116B (FIG. 3B) described above, except that magnetarray assembly 216 is a right-handed magnet array assembly 216, whereasmagnet array assembly 116B (FIG. 3B) is a left-handed magnet arrayassembly 116B. Magnet arrays B and D are elongated in the stage-ydirection, and each comprise a plurality of linearly-elongatedmagnetization segments 214 (see FIG. 10E) with magnetization directionsorthogonal to their stage-y elongation direction. Magnet arrays A and Care elongated in the stage-x direction, and each comprise a plurality oflinearly-elongated magnetization segments 214 (see FIG. 10E) withmagnetization directions orthogonal to their stage-x elongationdirection. Although FIG. 10E shows a y-magnet array 212B, it should beappreciated that x-magnet arrays A, may have characteristics similar tothose of the FIG. 10E y-magnet array 212B, with appropriate modificationto the directions.

In the particular case of the illustrated embodiment shown in FIG. 10A,x-magnet arrays A and C are each split by a middle plane oriented instage-y/stage-z direction to provide magnet array A with a pair ofx-sub-arrays 212A′ and to provide magnet array C with a pair ofx-sub-arrays 212C′. X-sub-arrays 212A′ of the FIG. 10 embodiment areoffset from one another in the stage-y direction by an amount λ/10 whichmay tend to attenuate fifth-order harmonic field distortion.X-sub-arrays 212C′ of the FIG. 10 embodiment are similarly offset fromone another in the stage-y direction by an amount λ/10 which may tend toattenuate fifth-order harmonic field distortion on the x-coil traces.Each x-sub-array 212A′, 212C′ of the FIG. 10 embodiment has astage-y-direction width W_(my) of λ and a stage-x direction length of2λ, although this is not necessary. Similarly, in the particular case ofthe illustrated embodiment shown in FIG. 10A, y-magnet arrays B and Dare each split by a middle plane oriented in stage-x/stage-z directionto provide magnet array B with a pair of y-sub-arrays 212B′ and toprovide magnet array D with a pair of y-sub-arrays 212D′. Y-sub-arrays212B′, 212D′ of the FIG. 10 embodiment may offset from one another inthe stage-x direction by an amount λ/10 which may tend to attenuatefifth-order harmonic field distortion on the y-coil traces. Eachy-sub-array 212B′, 212D′ of the FIG. 10 embodiment has astage-x-direction width W_(mx) of λ and a stage-y direction length of2λ, although this is not necessary. The division of magnet arrays A, B,C, D into offset sub-arrays 212A′, 212B′, 212C′, 212D′ is not necessary.In some embodiments, magnet arrays A, B, C, D are similar to any of theother elongated segment magnet arrays described herein. Magnet arrayassembly 216 may comprise a space 251 having dimensions Sx=Sy=λ betweenthe adjacent edges of its magnet arrays A, B, C, D and offsets Ox=Oy=λbetween corresponding edges of its magnet arrays A, B, C, D. Moveablestage 210 may comprise bumper components (not explicitly enumerated)similar to those described above for moveable stage 10.

FIG. 10B shows an x-trace layer 240 in a stator tile (excitation region)243 of a stator 230 which may be used in conjunction with the FIG. 10Amoveable stage 210. X-trace layer 240 of stator tile 243 comprises aplurality of x-trace groups 66, where each x-trace group 66 has astator-y direction width W_(gy)=λ and comprises a plurality of x-traces(not explicitly enumerated) which can be energized (i.e. into whichcurrents can be driven) independently of the other x-trace groups 66. Inone particular embodiment, each x-trace group 66 comprises six x-tracesconnected so that current can be driven into the six x-traces by onethree-phase amplifier 70 in a manner similar to that described above inconnection with FIG. 8B. FIG. 10C shows a y-trace layer 242 in a statortile (excitation region) 243 of a stator 230 which may be used inconjunction with the FIG. 10A moveable stage 210. Y-trace layer 242 ofstator tile 243 comprises a plurality of y-trace groups 68, where eachy-trace group 68 has a stator-x direction width W_(gx)=λ and comprises aplurality of y-traces (not explicitly enumerated) which can be energized(i.e. into which currents can be driven) independently of the othery-trace groups 68. In one particular embodiment, each y-trace group 68comprises six y-traces connected so that current can be driven into thesix y-traces by one three-phase amplifier 70 in a manner similar to thatdescribed above in connection with FIG. 8B. FIG. 10D shows a top view ofan overall stator tile 243 of stator 230, which comprise a plurality oftrace layers including x-trace layer 240 (FIG. 10B) and y-trace layer242 (FIG. 10C). In FIG. 10C, x-trace layer 240 and y-trace layer 242overlap with one another in the stator z-direction over the extent ofstator tile 243 in the stator-x/stator-y directions. The stator-zdirection order of x-trace layer 240 and y-trace layer 242 may beinterchanged in some embodiments. Additional x-trace layer(s) 240 and/ory-trace layer(s) may be provided in some embodiments.

FIG. 10E shows a stage-x/stage-z cross-sectional side view of magnetarray 212B (or one of its sub-arrays 212B′) in the FIG. 10A moveablestage 210. Comparing FIG. 10E to FIG. 3C, it can be seen that magnetarray 212B comprises features substantially similar to those of magnetarray 112B described above in connection with FIG. 3C. Magnet array 212Bcontains two edge magnetization segments 214 with widths that are halfthose of inner magnetization segments 214. In each sub-array 212B′ ofthe FIG. 10E embodiment, there are N_(t)=4 different magnetizationdirections, and the widths of inner magnetization segments 214 isλ/N_(t) and the widths of edge magnetization segments 214 is λ/2N_(t).Generally, N_(t) can be any integer number greater than 1. Eachsub-array 212B′ is symmetric about a plane 218 extending in stage-y andstage-z and passing through the stage-x dimension center of sub-array212B′. Other magnet arrays 212A, 212C, 212D of magnet array assembly 216may have similar features. Other than for their locations, thesub-arrays in one magnet array of magnet array assembly 216 may beidentical.

FIG. 11A shows a position sensing layer 84 corresponding to a statortile (excitation region) 243 of the FIG. 10 stator 230. Each positionsensing layer 84 corresponding to each stator tile 243 comprises aplurality (e.g. four in the case of the FIG. 11A embodiment) ofindependent position sensing regions 85. Each position sensing region 85may comprise a sensing system 80 similar to sensing system 8 describedabove in connection with FIG. 9. For example, in each position sensingregion 85, a plurality of magnetic field sensing elements 82 or othersuitable elements are distributed in a matrix format 83 to measuremoveable stage 210 positions (or other characteristics, as describedabove), independently from other position sensing regions 85. FIG. 11Bshows a side view of a stator tile 243, which includes a positionsensing layer 84 atop a number of coil trace layers 240, 242. Althoughposition sensing layer 84 is shown on the positive stator-z side of coiltrace layers 240, 242 in the FIG. 11 embodiment, this is not necessary.In some embodiments, position sensing layer 84 may additionally oralternatively be located on the negative stator-z side of coil tracelayers 240, 242 as described, for example, in Patent Cooperation Treatyapplication No. PCT/CA2014/050739.

FIG. 12 shows a non-limiting embodiment of a displacement device 250according to another particular embodiment of the invention.Displacement device 250 of the illustrated FIG. 12 embodiment comprisesa plurality (e.g. five in the case of the illustrated embodiment) ofmoveable stages 210 and a stator 230 comprising a plurality (e.g. fourin the case of the illustrated embodiment) of stator tiles (excitationregions) 243. Multiple stator tiles 243 can form a stator lane or otherpatterns (which may be arbitrary and which may be suited for particularapplications). In this description and the accompanying claims, a statorlane (or, for brevity, a lane) may be defined as a plurality of statortiles 243 arranged edge to edge and adjacent to one another to form aline in the stator-x or stator-y direction. In the particular case ofthe FIG. 12 example embodiment, stator 230 comprises a stator lane 244wherein the x-oriented edges of a plurality of stator tiles 243 arearranged to abut against one another to provide a stator lane 244 thatextends in a line in the stator-y direction. In FIG. 12 and thisdescription, individual moveable stages 210 and individual stator tiles243 may be indexed by an additional reference number to distinguishindividual moveable stages 210 and individual stator tiles 243 from oneanother, where such distinction is desired. For example, the individualmoveable stages 210 shown in the FIG. 12 example embodiment may beindividually referred to as moveable stages 210_1, 210_2, 210_3, 210_4and 210_5 and the individual stator tiles (excitation regions) 243 inthe FIG. 12 example embodiment may be referred to as stator tiles(excitation regions) 243_1, 243_2, 243_3, 243_4.

When any two moveable stages 210 of displacement device 250 are arranged(e.g. by controllable movement) without overlap in the stator-xdirection and without overlap in the stator-y direction (for example,moveable stages 210_2 and 210_3), each moveable stage 210 can becontrolled individually and independently in six degrees-of-freedom(DOF)—i.e. translation in x, y, and z and rotation about x, y and zaxes. In the particular case of the illustrated FIG. 12 embodiment, eachmoveable stage 210 comprises a plurality (e.g. 4) magnet arrays 212 andeach magnet array 212 is λ wide (across its elongation direction), andeach stator tile is 8λ by 8λ with a plurality (e.g. 4) independentposition sensing regions 85. In the particular case of the illustratedFIG. 12 embodiment, two moveable stages 210 of displacement device 250can be completely independently controlled provided that their magnetarray assemblies 216 have center-to-center spacing of not less than 4λin the stator-x direction and not less than 4λ in the stator-ydirection. Moveable stages 210 having this spacing may be referred toherein as being controllably adjacent. For example, moveable stage 210_2and moveable stage 210_3 are controllably adjacent.

By driving currents into suitable coil traces and thereby drivingmoveable stage 210 with reduced couplings, two moveable stages 210 maybe arranged (e.g. by controllable movement) to be overlapping in thestator-x direction or overlapping in the stator-y direction in a singlestator tile 243 and the motion (e.g. position) of such moveable stages210 can still be controlled in six degrees of freedom. For example, inthe illustrated moveable stage configuration shown in FIG. 12, moveablestage 210_1 and moveable stage 210_3 are overlapping in the stator-ydirection and the motion (e.g. position) of each of moveable stage 210_1and moveable stage 210_3 can be individually controlled in six degreesof freedom by driving currents into suitable coil traces and drivingmoveable stages 210_1, 210_3 with reduced couplings. To explain thesereduced couplings, we may adopt a convention where a magnet array A, B,C, D of a moveable stage 210_1, 210_2, 210_3, 210_4 may be referred tousing a combination of a letter (which refers to a magnet array) and anumber which refers to the index of the moveable stage. For example,magnet array B in moveable stage 210_3 may be referred to as magnetarray B3.

In the illustrated moveable stage configuration shown in FIG. 12, thestage-x/stage-y centers 269_1, 269_3 of the magnet array assemblies ofmoveable stages 210_1 and 210_3 are generally aligned with one anotherin the stator-y direction and are spaced apart from one another by adimension of stator tiles 243 in the stator-y direction. Even with thisalignment in the stator-y direction, the motion (e.g. position) of eachof moveable stage 210_1 and moveable stage 210_3 can be individuallycontrolled in six degrees of freedom, where there is sufficient spacingbetween the aligned moveable stages 210. For example, in the case of theillustrated FIG. 12 embodiment, the stator-y direction spacing of thecenters 269_1, 269_3 are spaced apart from one another by a dimension ofstator tiles 243 in the stator-y direction (or, in some embodiments, bywithin 10% of a dimension of stator tiles 243 in the stator-y direction;or, in some embodiments, by within 20% of a dimension of stator tiles243 in the stator-y direction) and this provides sufficient spacing forindependent motion control (in six degrees of freedom) of alignedmoveable stages 210_1, 210_3. In the case of the example FIG. 12embodiment, this control may be achieved by driving magnet array A1(magnet array A in moveable stage 1) with x-traces in stator tile 243_1,magnet array B1 with y-traces in stator tile 243_1, magnet array C1 withx-traces in stator tile 243_2, so that moveable stage 210_1 can be fullycontrolled in six DOF. Similarly, by driving magnet array A3 withx-traces in stator tile 243_2, driving magnet array B3 with y-traces instator tile 243_2, and driving magnet array C3 with x-traces in statortile 243_3, the motion (e.g. position) of moveable stage 210_3 can befully controlled in six degrees of freedom.

It may be observed from FIG. 12 that there may be some cross-coupling offorces onto magnet arrays B1 and B3 by the currents driven into the twoy-trace groups of stator tile 243_2 that exert force on magnet array B3,since a portion of magnet array B1 overlaps this same pair of y-tracegroups of stator tile 243_2 in the stator-z direction. Magnet arrays B1and B3 may be said to “share” these coil trace groups. In general, twomagnet arrays 212 elongated in the same direction (e.g. two x-magnetarrays 212 or two y-magnet arrays 212) may be said to “share” a coiltrace group if the coil traces in the coil trace group are elongatedgenerally in the same direction as the two magnet arrays 212 and bothmagnet arrays 212 overlap corresponding portions of the shared coiltrace group in the stator-z direction. In some embodiments orapplications, the control techniques described herein may be used wherethe two magnet arrays 212 which share a coil trace group both overlap(in the stator-z direction) at least one individual coil trace withinthe shared coil trace group. Magnet arrays 212 which share a coil tracegroup experience forces which are coupled to one another when current isdriven into the shared coil trace group. While magnet arrays B1 and B3share two y-trace groups, the proportion of magnet array B1 thatoverlaps these y-trace groups of stator tile 243_2 in the stator-zdirection is relatively small compared to the proportion of magnet arrayB3 that overlaps these y-trace groups of stator tile 243_2 in thestator-z direction. Consequently, the force on magnet array B1 caused bythe currents in these shared y-traces may be relatively small andsuitable control algorithms can be designed to accommodate such smallcross-coupling forces. For example, if we consider the y-trace group68_1 shared by B1 and B3 in FIG. 12, it can be observed that a portionP₁ of the area (planar area extending in the stator-x and stator-ydirections) of coil array B1 overlaps shared y-trace group 68_1 in thestator-z direction and that a significantly larger portion P₃ of thearea of coil array B3 overlaps shared y-trace group 68_1 in the stator-zdirection. The currents driven into shared y-trace group 68_1 can bedetermined based on the positions of both magnet arrays B1 and B3 (orthe positions of both of their corresponding moveable stages 210_1,210_3) as determined by feedback 63. However, because of the differentamounts of overlap (i.e. the different sizes of P₁ and P₃) the currentsdriven into shared y-trace group 68_1 can be determined based, to arelatively large extent, on desired forces for magnet array B3 and, to arelatively small extent, on desired forces for magnet array B1. In oneexample, currents driven into shared y-trace group 68_1 can bedetermined by a weighted force F_(w) given by

$F_{w} = {{\frac{P_{3}}{P_{1} + P_{3}}F_{3}} + {\frac{P_{1}}{P_{1} + P_{3}}F_{1}}}$

according to a suitable commutation algorithm, where F₁ is a desiredforce to be imparted on magnet array B1 (determined based on thefeedback position of moveable stage 210_1 using a suitable feedbackcontrol method) and F₃ is a desired force to be imparted on magnet arrayB3 (determined based on the feedback position of moveable stage 210_3using a suitable feedback control method). Examples of suitablecommutation algorithm and suitable position feedback control method arediscussed in PCT application No. PCT/CA2012/050751. When moveable stages210_1 and 210_3 are moving in the positive or negative stator-ydirection while maintaining roughly the same stator-y directionseparation, the portions P₁ and P₃ will also change, and, consequently,so does the relation of F_(w) to F₃ and F₁. It will be appreciated bythose skilled in the art that magnet arrays B1 and B3 also share y-tracegroup 68_2 and that a weighted force relationship may be similarlyobtained for y-trace group 68_2. More generally, it will also beappreciated that the above weighted force relationship may be suitablymodified where different magnet arrays share a coil trace group.

Magnet array D1 and D3 also share two y-trace groups in tile 243_2. Likemagnet arrays B1 and B3, any current driven into either of the y-tracegroups of stator tile 243_2 shared by magnet arrays D1 and D3 createscoupled forces in magnet arrays D1 and D3. A difference between thesituation of magnet arrays D1 and D3 (relative to magnet arrays B1 andB3), is that the portions of magnet arrays D1 and D3 that overlap theshared y-trace groups of stator tile 243_2 in the stator-z direction arerelatively similar to one another, whereas the portions of magnet arraysB1 and B3 that overlap the shared y-trace groups of stator tile 243_2 inthe stator-z direction are relatively dis-similar. This similarity inthe portions of magnet arrays D1 and D3 that overlap the shared y-tracegroups of stator tile 243_2 can be seen from FIG. 12 by observing thesimilarity in the portions P₁, P₃ of magnet arrays D1, D3 that overlapshared y-trace group 68_3, respectively. In some embodiments orapplications, controller 60 may be configured to use a suitablesimilarity threshold to determine whether the portions of magnet arraysthat overlap shared coil trace groups are dis-similar (like magnetarrays B1, B3 of FIG. 12) or similar (like magnet arrays D1, D3 of FIG.12). Such similarity thresholds may be evaluated based on feedbackinformation 63 obtained by controller 60 (see FIG. 8A) relating to thepositions of both moveable stages 210 having magnet arrays 212 thatshare a coil trace group. For example, in the case of the illustratedembodiment of FIG. 12, a similarity threshold evaluation for y-tracegroup 68_1 may be based on the ratio P₁/P₃ and a suitable threshold P*.For example, if P₁/P3 is in a range of 1−P*<P₁/P3<1+P*, then theoverlapping portions P₁, P₃ of magnet arrays B1, B3 may be considered tobe similar and, otherwise, the overlapping portions P₁, P₃ of magnetarrays B1, B3 may be considered to be dis-similar. In some embodiments,where the portions of magnet arrays that overlap a shared coil tracegroup are determined to be dis-similar (like magnet arrays B1, B3 in theFIG. 12 example), currents may be controllably driven into the sharedcoil-trace group based on the positions of both of the correspondingmoveable stages (e.g. from feedback). In some embodiments, where theproportions of magnet arrays that overlap shared coil trace groups aredetermined to be similar (e.g. like magnet arrays D1, D3 in the FIG. 12example), no current is driven in the corresponding shared coil tracegroups. In some embodiments, where the proportions of magnet arrays thatoverlap shared coil trace groups are determined to be similar (e.g. likemagnet arrays D1, D3 in the FIG. 12 example), currents can be driveninto the shared coil trace groups by commanding feed-forward (open-loop)currents and corresponding feed-forward (open-loop) forces. Suchopen-loop currents and the corresponding forces may help to reducecurrent/force requirements associated with other magnet arrays (e.g. toachieve performance objectives). Since where the proportions of magnetarrays that overlap shared coil trace groups are determined to besimilar (e.g. like magnet arrays D1, D3 in the FIG. 12 example), dynamiccoupling between such magnet arrays D1, D3 (and their correspondingmoveable stages 210_1, 210_3) can be avoided by refraining from usingposition feedback control for currents driven into shared coil tracegroups—i.e. the current control signals output by controller 60 for thecoil trace currents corresponding to the shared coil trace groups aredetermined independently of position feedback related to the position ofthe moveable stages 210.

Particular embodiments provide methods and systems for controlling aplurality (e.g. first and second) moveable stages 210 on a particulartile. In some embodiments, where a magnet array 212 from a firstmoveable stage 210 and a magnet array 212 from a second moveable stage210 both overlap a shared group of coil traces in the stator-zdirection, the currents driven into the shared group of coil traces andused to create forces on overlapping magnet arrays 212 of the first andsecond moveable stages 210 can be controlled based at least in part onthe positions of both first and second moveable stages 210. For example,controller 60 may controllably drive currents into the shared group ofcoil traces which are based at least in part on the positions of bothfirst and second moveable stages 210. In some embodiments, the currentsused to create forces on first and second moveable stages 210 can becontrolled to cause first and second moveable stages 210 to pass oneanother on a stator lane 244 comprising a single row or column of one ormore stator tiles 243, without using other stator lanes 244 and/orstator tiles 243. Allowing moveable stages 210 to pass one another isparticularly important when moveable stage sequence needs to be changed.

FIGS. 13A-13G (collectively, FIG. 13) illustrate a method forcontrollably moving first and second moveable stages 210_1, 210_2 topass one another in a stator lane 244 having a width of a single tile243 (or to pass one another on a single tile) according to a particularembodiment. In addition to referring to individual magnet arrays 212 asmagnet arrays A1,B1,C1,D1 and A2,B2,C2,D2 (as discussed above), thisdescription of FIG. 13, for convenience, refers to individual x-tracegroups (referred to using reference number 66 at other places herein) asx-trace groups X1, X2, X3, . . . . In the illustrated example embodimentof FIG. 13, stator tile 243 comprises eight x-trace groups, X1, X2, X3,. . . X8. Moveable stage 210_1 may be assumed (without loss ofgenerality) to originally be traveling in the negative stator-ydirection and moveable stage 210_2 may be similarly assumed to betraveling in the positive stator-y direction and it is assumed that itis desired to have moveable stage 210_1 and 210_2 pass one another inthe stator-y direction (i.e. to change their relative positions in thestator-y direction). In a first stage or step illustrated in FIG. 13A,first and second moveable stages 210_1, 210_2 do not overlap one anotherin the stage-x direction. Moveable stage 210_1 moves in the negativestator-y direction toward meeting plane 246 (extending in the stator-xand stator-z directions and shown as a dashed line in FIG. 13) andmoveable stage 210_2 moves in the positive stator-y direction towardmeeting plane 246. Each of moveable stages 210_1, 210_2 may becontrollably moved to have the same speed v_(m), although this is notnecessary. In the FIG. 13A configuration, each moveable stage 210_1,210_2 can be actuated with eight independent forces (i.e. twoindependent forces (either x and z oriented forces; or y and z orientedforces) on each array 212 of each moveable stage 210).

FIG. 13B illustrates a second stage or step where moveable stages 210_1,210_2 start to overlap one another in the stator-x direction. In theparticular case of the illustrated embodiment of FIG. 13B, magnet arraysA2 and C1 start to overlap one another in the stator-x direction and mayshare x-trace groups X4 and/or X5. In some embodiments, when magnetarrays A2 and C1 start to overlap one another in the stator-x direction(as is the case in FIG. 13B), only three magnet arrays 212 on eachmoveable stage 210_1, 210_1 have currents driven into theircorresponding coil trace groups. Coil traces or coil trace groups may besaid to correspond to a magnet array 212 (or vice versa) when the coiltraces or coil trace groups and the magnet array 212 overlap one anotherin the stator-z direction. In some embodiments, in the particular caseof the FIG. 13B configuration, only three magnet arrays 212 on eachmoveable stage 210_1, 210_2 have currents driven into theircorresponding coil trace groups. In particular, currents are driven intothe coil trace groups corresponding to magnet arrays A1, B1, D1, B2, C2,D2, and, in some embodiments, no currents are driven into the x-tracegroups X4, X5 corresponding to, and shared by, magnet arrays C1, A2,since such currents may cause cross-coupling of forces between magnetarrays C1, A2. In some embodiments, rather than driving no currents intox-trace groups X4, X5, x-trace groups X4, X5 may be driven open-loopwith the same non-zero currents (e.g. for the case of three-phasecurrents, phase A driven into x-trace group X4 is the same current asphase A driven into x-trace group X5; phase B driven into x-trace groupX4 is the same current as phase B driven into x-trace group X5; phase Cdriven into x-trace group X4 is the same current as phase C driven intox-trace group X5). The FIG. 13B configuration may last until magnetarrays A1 and A2 start to overlap one another in the stator-x direction.

FIG. 13C shows a third step or configuration, where magnet arrays A1 andA2 (and also magnet arrays C1 and C2) start to overlap one another inthe stator-x direction. In the particular case of the illustratedembodiment of FIG. 13C, magnet arrays A1, A2 start to overlap oneanother in the stator-x direction and may share (i.e. overlap in thestator-z direction with) x-trace groups X5 and/or X6 and magnet arraysC1, C2 start to overlap one another in the stator-x direction and mayshare (i.e. overlap in the stator-z direction with) x-trace groups X3and X4. As shown in FIG. 13C, while the x/y centers 269_1, 269_2 of bothmoveable stages 210_1, 210_2 have not yet passed notional meeting line246, we can define the width (as measured in the stator-y direction)which magnet arrays A1 and A2 overlap one another in the stator-xdirection to be ηλ, where η is an overlapping factor (either a fraction0<η≤1 or a percentage 0%<η≤100%) and λ is the width (as measured in thestator-y direction) of magnet array A1 and A2. As noted above, in someembodiments, x-magnet arrays A1, A2 may be provided with y directionwidths W_(my) which need not be equal to λ. In such embodiments, thewidth (as measured in the stator-y direction) which magnet arrays A1 andA2 overlap one another in the stator-x direction may be ηW_(my), where ηis an overlapping factor (either a fraction 0<η≤1 or a percentage0%<η≤100%) and W_(my) is the width (as measured in the stator-ydirection) of magnet array A1 and A2. It will be appreciated that η is afunction of the positions of moveable stages 210_1, 210_2 (or theirmagnet arrays A1, A2) and is particularly related to their stator-ypositions. For 0<η<η*, where η* is a suitable threshold (e.g. greaterthan 50% in some embodiments, greater than 70% in some embodiments,greater than 80% in some embodiments and greater than 90% in someembodiments): a proportion (1−η/2) of the stage-y dimension of magnetarray A1 corresponds to (i.e. overlaps in the stator-z direction with)x-trace group X6 (see FIG. 13C) and the remaining proportion (η/2) ofthe stage-y dimension of magnet array A1 corresponds to x-trace groupX5; and a proportion (1−η/2) of the stage-y dimension of magnet array A2corresponds to (i.e. overlaps in the stator-z direction with) x-tracegroup X5 and the remaining proportion (η/2) of the stage-y dimension ofmagnet array A2 corresponds to x-trace group X6. In the particular caseof the illustrated embodiment shown in FIG. 13C, the entire stage-xdimensions of magnet arrays A1, A2 overlap the shared x-trace groups X5,X6 and, as a result, the above-described proportions of the stage-ydimensions of magnet arrays A1, A2 correspond to similar proportions ofthe areas of magnet arrays A1, A2. The threshold η* may be configurable(e.g. operator configurable) in some embodiments.

In the FIG. 13C configuration, currents in x-trace groups X5 and X6 canbe controllably driven in such a way that two independent (y and zoriented) forces are generated on magnet array A1 and another twoindependent (y and z oriented) forces are generated on magnet array A2.In the FIG. 13C configuration, where 0<η<η*, controller 60 determinesthe currents driven into coil trace groups X5, X6 (i.e. the coil tracegroups shared by magnet arrays A1, A2) based on the positions of bothmoveable stages 210_1 and 210_2 (i.e. the moveable stages comprising theoverlapping magnet arrays Al and A2) and causes these currents to bedriven into the shared coil trace groups X5, X6. This contrasts withconventional control of a single moveable stage, where the currents usedto controllably move the single moveable stage are based only on theposition of the single moveable stage. In the case of the FIG. 13Cconfiguration, in some embodiments, controller 60 may determine thecurrents to be driven into the shared coil trace group X6 based on aproportion (1−η/2) of a stage-y dimension of magnet array A1 thatoverlaps with the shared coil trace group X6 in the stator-z directionand based on a proportion η/2 of a stage-y dimension of magnet array A2that overlaps with shared coil trace group X6 in the stator-z direction.Similarly, in the case of the FIG. 13C configuration, in someembodiments, controller 60 may determine the currents to be driven intothe shared coil trace group X5 based on a proportion η/2 of a stage-ydimension of magnet array A1 that overlaps with the shared coil tracegroup X5 in the stator-z direction and based on a proportion (1−η/2) ofa stage-y dimension of magnet array A2 that overlaps with shared coiltrace group X5 in the stator-z direction. The currents driven intoshared x-trace groups X5, X6 may be determined based on the desiredforce to be applied to magnet array A1, the desired force to be appliedto magnet array A2 and the positions (e.g. as determined by feedback) ofmoveable stages 210_1, 210_2. The desired forces on magnet arrays A1 andA2 may be determined from their respective position control algorithmswhich may control the motion of their respective movers 210_1, 210_2 insix degrees of freedom. For example, in the case of shared x-trace groupX5, P₁ represents the portion of magnet array A1 that overlaps x-tracegroup X5 and P₂ represents the portion of magnet array A2 that overlapsx-trace group X5. It will be appreciated that P₁ and P₂ depend on thepositions of moveable stages 210_1, 210_2. Like the above-describedsituation in FIG. 12, the currents driven into the shared coil trace X5can be determined according to a weighted force

$F_{w} = {{\frac{P_{2}}{P_{1} + P_{2}}F_{2}} + {\frac{P_{1}}{P_{1} + P_{2}}F_{1}}}$

according to a suitable commutation algorithm, where F₁ is the desiredforce on magnet array A1 calculated based on feedback positions ofmoveable stage 210_1 using a suitable position feedback control method,F₂ is the desired force on magnet array A2 calculated based on feedbackpositions of moveable stage 210_2 using a suitable position feedbackcontrol method. Examples of suitable commutation algorithm and suitableposition feedback control method are discussed in PCT application No.PCT/CA2012/050751. In general, the current for a coil trace groupcurrent may be determined from a desired weighted force F_(w) accordingto a commutation law, the weighted force F_(w) may be determined fromF₁, F₂ (for FIG. 13C case), F₁ and F₂ are desired forces on magnetarrays A1 and A2 which may be determined from the positions of moveablestages 210_1, 210_2 (e.g. from feedback). When moveable stages 210_1 and210_2 are moving in the negative stator-y and positive stator-ydirections respectively, P₁ and P₂ will also change accordingly, and sodoes the relation of F_(w) to F₂ and F₁. In the particular case of theFIG. 13C situation, the entire stage-x dimension lengths of magnetarrays A1, A2 overlap the shared coil trace group X5 and are equal toone another. Consequently, the relative overlapping portions P₁, P₂ maybe reduced to the above-discussed proportions, where P₁ is proportionalto η/2 and P₂ is proportional to (1−η/2), such that the above weightedforce formula for x-trace group X5 reduces to F_(w)=(1−η/2)F₂+η/2 F₁ Itwill be appreciated that analogous control techniques may be used todetermine the currents for the shared x-trace group X6.

Similarly, currents in shared x-trace groups X3 and X4 can be determinedbased on the positions of moveable stages 210_1, 210_2 and driven insuch a way that two independent forces are generated on magnet array C1and two independent forces are generated on magnet array C2. As aresult, in the configuration of FIG. 13C (e.g. with x-magnet arrays A1,A2 overlapping in the stator-x direction and x-magnet arrays C1, C2overlapping in the stator-x direction), the motion (e.g. positions) ofmoveable stages 210_1, 210_2 can still be controlled with six degrees offreedom with suitably controlled currents and suitably controlled forcesbeing applied to each of the magnet arrays 212 of each moveable stage210_1, 210_2. In particular, moveable stage 210_1 can still becontrollably forced in the negative stator-y direction and moveablestage 210_2 can still be controllably forced in the positive stator-ydirection.

When moved in this manner, moveable stages eventually reach thethreshold overlap factor η*—i.e. where the overlap factor η betweenmagnet arrays A1, A2 or between magnet arrays C1, C2 is in a range ofη*≤η≤1. The configuration corresponding to this next step isschematically illustrated in FIG. 13D. In the FIG. 13D configuration,where η*≤η≤1, x-trace groups X5 and X6 may be driven open-loop with thesame non-zero currents (e.g. for the case of three-phase currents, phaseA driven into x-trace group X5 is the same current as phase A driveninto x-trace group X6; phase B driven into x-trace group X5 is the samecurrent as phase B driven into x-trace group X6; phase C driven intox-trace group X5 is the same current as phase C driven into x-tracegroup X6). Driving these same non-zero currents can be used to generatea feed-forward (open-loop) stator-z oriented force as if η=1 or η=100%.Such open-loop currents driven into x-trace groups X5, X6 may be thesame (and not changing relative to one another) throughout the FIG. 13Dconfiguration where η*≤η≤1. Similarly methods may be used to drive thesame open-loop non-zero currents into x-trace groups X3, X4 to therebydrive magnet arrays C1, C2. In some embodiments, for the configurationwhere η*≤η≤1, the currents driven into the coil-trace groups (e.g. X5,X6 and/or X3, X4) shared by magnet arrays that overlap one another in astator direction (e.g. A1, A2 and/or C1, C2) may be set to zero. In theFIG. 13D configuration, where η*≤η≤1, first and second moveable stages210_1, 210_2 may continue to travel in the respective directions thatthey were traveling prior to the FIG. 13D configuration (e.g. firstmoveable stage 210_1 may continue to travel in the negative stator-ydirection and second moveable stage 210_2 may continue to travel in thepositive stator-y direction) and may pass each other due to theirmomentum. During the FIG. 13D configuration, where η*≤η≤1, controller 60may continue to controllably drive currents into the y-trace groupscorresponding to magnet arrays B1, D1 and B2, D2 and may thereby controlthe motion (e.g. position) of each moveable stage 210_1, 210_2 with 4degrees of freedom. For example, in the case of the illustratedembodiment of FIG. 13D, controller 60 could still controllably drivecurrents into the y-trace groups corresponding to magnet arrays B1, D1and B2, D2 to control the translation in (x,z) and rotation in (ry_(r),rz_(r)). Further, rotation motion around the y axis (i.e. ry_(r)) may bepassively stabilized by the open-loop non-zero currents driven intox-coil trace groups X3, X4, X5, X6.

The FIG. 13D situation continues until η=1 or η=100%, which correspondsto the situation where magnet arrays A1, A2 substantially completelyoverlap one another in the stator-x direction and magnet arrays C1, C2substantially completely overlap one another in the stator-x direction.Due to the continued momentum of moveable stages 210_1, 210_2 maycontinue to travel in the respective directions that they were travelingprior to the FIG. 13D configuration (e.g. first moveable stage 210_1 maycontinue to travel in the negative stator-y direction and secondmoveable stage 210_2 may continue to travel in the positive stator-ydirection). Accordingly, once the overlap factor reaches η=1 or η=100%,the overlap factor η will start to reduce as the centers 269_1, 269_2 ofmoveable stages 210_1, 210_2 pass notional meeting line 246. In thecircumstance where η is decreasing and η*≤η≤1, controller 60 may beconfigured to use the same current driving techniques as those discussedabove for FIG. 13D (i.e. where the only difference is that η isincreasing in the FIG. 13D context).

At some stage, the overlap factor η may again fall back below thethreshold value This step or configuration is shown in FIG. 13E, where0<η<η*. In the FIG. 13E configuration: a proportion (1−η/2) of thestator-y dimension of magnet array A1 corresponds to (i.e. overlaps inthe stator-z direction with) x-trace group X5 (see FIG. 13E) and theremaining proportion (η/2) of the stator-y dimension of magnet array A1corresponds to x-trace group X6; and a proportion (1−η/2) of thestator-y dimension of magnet array A2 corresponds to (i.e. overlap inthe stator-z direction with) x-trace group X6 and the remainingproportion (η/2) of the stator-y dimension of magnet array A2corresponds to x-trace group X5. In the particular case of theillustrated embodiment shown in FIG. 13E, the entire stage-x dimensionsof magnet arrays A1, A2 overlap the shared x-trace groups X5, X6 and, asa result, the above-described proportions of the stage-y dimensions ofmagnet arrays A1, A2 correspond to similar proportions of the areas ofmagnet arrays A1, A2. The threshold η* may be configurable (e.g.operator configurable) in some embodiments. In this regard, the FIG. 13Estep/configuration is similar to that of FIG. 13C, where currents inx-trace groups X5 and X6 can be controllably determined and driven usingtechniques analogous to those described above in connection with FIG.134C and in such a way that two independent (y and z oriented) forcesare generated on magnet array A1 and another two independent (y and zoriented) forces are generated on magnet array A2. In the FIG. 13Econfiguration, where 0<η<η*, controller 60 determines the currentsdriven into coil trace groups X5, X6 (i.e. the coil trace groups sharedby magnet arrays A1, A2) based on the positions of both moveable stages210_1 and 210_2 (i.e. the moveable stages comprising the overlappingarrays A1 and A2) and causes these currents to be driven into the sharedcoil trace groups X5, X6. This contrasts with conventional control of asingle moveable stage, where the currents used to controllably move thesingle moveable stage are based only on the position of the singlemoveable stage. In some circumstances, controller 60 may determine thecurrents to be driven into the shared coil trace groups X5, X6 based ona proportion (1−η/2) of a stage-y dimension of magnet array A1 thatoverlaps with the shared coil trace group X5 in the stator-z directionand based on a proportion η/2 of a stage-y dimension of magnet array A2that overlaps with shared coil trace group X5 in the stator-z direction.Similarly, currents in shared x-trace groups X3 and X4 can be determinedand driven in such a way that two independent forces are generated onmagnet array C1 and two independent forces are generated on magnet arrayC2. As a result, in the configuration of FIG. 13E (e.g. with x-magnetarrays A1, A2 overlapping in the stator-x direction and x-magnet arraysC1, C2 overlapping in the stator-x direction), the motion (e.g. thepositions) of moveable stages 210_1, 210_2 can still be controlled withsix degrees of freedom with suitably controlled currents and suitablycontrolled forces being applied to each of the magnet arrays 212 of eachmoveable stage 210_1, 210_2. In particular, moveable stage 210_1 canstill be controllably forced in the negative stator-y direction andmoveable stage 210_2 can still be controllably forced in the positivestator-y direction.

As moveable stage 210_1 continues to move in the negative stator-ydirection and moveable stage 210_2 continues to move in the positivestator-y direction, moveable stages 210_1, 210_2 may reach theconfiguration of FIG. 13F, where magnet arrays A1, A2 no longer overlapand magnet arrays C1, C2 no longer overlap, but where magnet arrays A1and C2 overlap with one another in the stator-x direction. This FIG. 13Fstep or configuration may be similar to that of FIG. 13B describedabove, except that rather than magnet arrays C1 and A2 overlapping inthe stator-x direction (as was the case in FIG. 13B), magnet arrays A1and C2 overlap in the configuration of FIG. 13F. Control strategiesanalogous to those discussed above in connection with FIG. 13B may beemployed in the circumstances of FIG. 13F. In particular, in someembodiments, in the FIG. 13F configuration, only three magnet arrays 212on each moveable stage 210_1, 210_2 have currents driven into theircorresponding coil trace groups. In particular, currents are driven intothe coil trace groups corresponding to magnet arrays C1, B1, D1, A2, B2,D2, and, in some embodiments, no currents are driven into the x-tracegroups X4, X5 corresponding to, and shared by, magnet arrays A1, C2,since such currents may cause cross-coupling of forces between magnetarrays A1, C2. In some embodiments, rather than driving no currents intox-trace groups X4, X5, x-trace groups X4, X5 may be driven open-loopwith the same non-zero currents (e.g. for the case of three-phasecurrents, phase A driven into x-trace group X4 is the same current asphase A driven into x-trace group X5; phase B driven into x-trace groupX4 is the same current as phase B driven into x-trace group X5; phase Cdriven into x-trace group X4 is the same current as phase C driven intox-trace group X5).

While it was not discussed above in connection with the FIG. 13Bconfiguration, in some embodiments, either of the FIGS. 13B and 13Fconfigurations could use a control strategy similar to that describedabove for the configurations shown in FIGS. 13C, 13D and 13E. Forexample, an overlap factor η and an overlap threshold η* could bedefined between the overlapping magnet arrays (C1, A2 in the case ofFIG. 13B; and A1, C2 in the case of FIG. 13F) and then controlstrategies similar to those discussed above for FIGS. 13C, 13D and 13Ecould be used for the circumstances where 0<η<η* and η is increasing(analogous to FIG. 13C), where η*≤η≤1 (analogous to FIG. 13D) and where0<η<η* and η is decreasing (analogous to FIG. 13E).

The FIG. 13E configuration may last until magnet arrays A1 and C2 are nolonger overlapping one another in the stator-x direction, in which casemoveable stages 210_1, 210_2 are in the configuration shown in FIG. 13G,which is analogous to that shown in FIG. 13A, where each moveable stage210_1, 210_2 can be actuated with eight independent forces (i.e. twoindependent forces (either x and z oriented forces; or y and z orientedforces) on each array 212 of each moveable stage 210).

FIGS. 14A and 14B (collectively FIG. 14) show queuing formations formultiple moveable stages 210 of the FIG. 10 displacement device 250 andmethods for moving such moveable stages 210 into and out of such queuingformations according to particular embodiments. A queuing operation maybe considered to comprise moving a plurality of moveable stages 210 intoqueuing formation where the moveable stages 210 are densely packed. Itmay be desirable for controller 60 to be able to controllably moveindividual moveable stages 210 into and out of a queuing formationwithout external (e.g. human or other machine) intervention. In someembodiments, as shown in the illustrated example of FIG. 14A, four (oreven more) moveable stages 210 may be queued on a single stator tile 243(see moveable stages 210_1, 210_2, 210_3, 210_4 or stator tile 243_1 ofFIG. 14A). The motion (e.g. position) of each moveable stage 210 queuedon stator tile 243_1 is still fully controllable in six degrees offreedom and can be controllably moved (by controller 60) into and out ofthe queue on stator tile 243_1 as explained in more detail below. Inaddition to the high density of moveable stages in the FIG. 14A queue,moveable stages 210 on the periphery of the queue can move out of theFIG. 14A queue from four sides (±stator-x and ±stator-y) of the overallqueue, instead of only two ends in a conventional linear transportationsystem. Moveable stages 210 can similarly merge into the queue from foursides of the queue.

As shown in FIG. 14B, 4 moveable stages 210_1, 210_2, 210_3, 210_4 areon a single stator tile 243. Moveable stages 210 may be said to be on astator tile 243 if their magnet array assemblies overlap the stator tile243 in the stator-z direction. In the FIG. 14 embodiment, moveablestages 210 and stator tiles 243 have the features of moveable stage 210and stator tile 243 discussed above in connection with FIG. 10. Thex-trace groups and y-trace groups of stator tile 243 are respectivelyreferred to as x-trace groups X1, . . . , X8 and y-trace groups Y1, . .. , Y8. Due to space 251 between the x-magnet arrays A, C and they-magnet arrays B, D (see FIG. 10A), controller 60 can controllably movemoveable stages into the queue pattern shown in FIG. 14B. In the queuepattern shown in FIG. 14B, a dedicated coil trace group may be used todrive each magnet array in the four moveable stages 210. In the case ofmoveable stage 210_3 of the FIG. 14B example, currents driven intox-trace group X7 apply force to magnet array A3, currents driven intox-trace group X5 apply force to magnet array C3, currents driven intoy-trace group Y2 apply force to magnet array B3 and currents driven intoy-trace group Y4 apply force to magnet array D3. None of these coiltrace groups (X7, X5, Y3, Y4) are shared with the magnet arrays 212 ofother moveable stages 210_1, 210_2, 210_4. In fact, in the FIG. 14Bconfiguration, no two magnet arrays 212 share a coil trace group. Ally-magnet arrays have no overlap in the stator y-direction, and allx-magnet arrays have no overlap in the stator-x direction. As a result,two independent forces (either x and z oriented forces; or y and zoriented forces) can be generated on each magnet array 212 and themotion (e.g. position) of each of moveable stages 210 may be controlledwith six degrees of freedom.

In the FIG. 14B configuration, moveable stage 210_1 is an outerperipheral moveable stage in the sense that, of the movable stages shownin FIG. 14B, moveable stage 210_1 is the furthest in the negativestator-x direction and the furthest in the negative stator-y direction.Controller 60 may controllably move moveable stage 210_1 in the negativestator-x direction or in the negative stator-y direction to leave theFIG. 14B queue. In some embodiments, for moveable stage 210_1 to leavethe queue in the negative stator-x direction, only magnetic arrays A1,Bl, and C1 have current driven into their corresponding coil tracegroups X3, Y1, X1. No force is needed on magnet array D1 and, in someembodiments, no current need be driven into the coil trace groupscorresponding to magnet array D1. This avoids the potential for magnetarrays B3 and D1 to share coil trace groups. In some embodiments, any ofthe other techniques for addressing shared coil trace groups describedherein may be used to drive current into the coil trace groupscorresponding to magnet array D1. In some embodiments, as moveable stage210_1 is being moved out of the queue in the negative stator-xdirection, currents may be driven into the coil trace groups X7, Y4, X5corresponding to magnetic arrays A3, D3, C3 of moveable stage 210_3. Noforce is needed on magnet array B3 and, in some embodiments, no currentneed be driven into the coil trace groups corresponding to magnet arrayB3. This avoids the potential for magnet arrays B3 and D1 to share coiltrace groups. In some embodiments, any of the other techniques foraddressing shared coil trace groups described herein may be used todrive current into the coil trace groups corresponding to magnet arrayB3. Similar techniques could be used to controllably move moveable stage210_1 out of the queue in the negative stator-y direction. Controllablymoving moveable stages into the queue is analogous to the procedure ofmoving moveable stages out of the queue.

In the FIG. 14B configuration, moveable stage 210_3 is an innerperipheral moveable stage in both the stator-x and stator-y directionsin the sense that, of the movable stages shown in FIG. 14B, moveablestage 210_3 is on the periphery of the queue, but moveable stage 210_1is further in the negative stator-x direction and moveable stage 210_4is further in the positive stator-y direction. When it is desired tomove moveable stage 210_3 out of the queue in the positive stator-ydirection, the following steps may be used: (1) controllably move outerperipheral movable stage 210_4 out of the queue in the positive stator-ydirection (e.g. onto a different stator tile 243 (not shown)) using atechnique analogous to that discussed above for moving outer peripheralmoveable stage 210_1 out of the queue; (2) controllably move innerperipheral movable stage 210_3 out of the queue in the positive stator-ydirection (e.g. onto a different stator tile 243 (not shown)) using atechnique analogous to that discussed above for moving outer peripheralmoveable stage 210_1 out of the queue; (3) controllably move moveablestages 210_3 and 210_4 to pass one another in the stator-y direction asdescribed above in connection with FIG. 13; (4) controllably movemoveable stage 210_4 back into the queue.

Generally, the methods described herein corresponding to FIGS. 12-14 canbe applied to moveable stages having other suitable magnet arraygeometries and stators having other suitable coil trace structures, withsuitable modification.

In one embodiment of the invention, three out of four magnet arraysoverlap in the stator-z direction with their corresponding coil tracegroups and currents are controllably driven into these correspondingcoil trace groups to generate forces which may be used to control themotion (e.g. the position) of a moveable stage with six degrees offreedom. In some embodiments, no currents are driven in the coil tracegroups corresponding to the fourth magnet array and no correspondingforce is generated on the fourth magnet array. In some embodiments,others of the techniques for addressing shared coil trace groupsdescribed herein may be used in conjunction with the fourth magnetarray.

In one embodiment of the invention, four moveable stages are denselyaccumulated on a stator coil tile, any two y-magnet arrays of thesemoveable stages have stator-y direction overlapping width less than1/9λ, any two x-magnet arrays of these moveable stages have statorx-direction overlapping width less than 1/9λ; each moveable stageoverlaps with at least one moveable stage in the stator-x direction withat least 2λ width, and overlaps with another moveable stage in thestator-y direction with at least 2λ width; the overall size of thestator tile is not greater than 9λ by 9λ; each moveable stage can becontrolled in 6-DOF.

In one embodiment of the invention, four moveable stages are denselyaccumulated on a stator coil tile, any two y-magnet arrays of thesemoveable stages have stator-y direction overlapping width less than1/9λ, any two x-magnet arrays of these moveable stages have stator-xdirection overlapping width less than 1/9λ; each moveable stage overlapswith at least one moveable stage in the stator-x direction with at least2λ width, and overlaps with another moveable stage in the stator-ydirection with at least 2λ width; the overall size of the stator tile isnot greater than 10λ by 10λ; each moveable stage can be controlled in6-DOF.

In one embodiment of the invention, four moveable stages are denselyaccumulated on a stator coil tile, any two y-magnet arrays of thesemoveable stages have stator-y direction overlapping width less than1/9λ, any two x-magnet arrays of these moveable stages have stator-xdirection overlapping width less than 1/9λ; each moveable stage overlapswith at least one moveable stage in the stator-x direction with at least2λ width, and overlaps with another moveable stage in the stator-ydirection with at least 2λ; the overall size of the stator tile is notgreater than 8λ by 8λ; each moveable stage can be controlled in 6-DOF.

In one embodiment of the invention, three moveable stages are denselyaccumulated on a stator coil tile, any two y-magnet arrays of thesemoveable stages have stator-y direction overlapping width less than1/9λ, any two x-magnet arrays of these moveable stages have stator-xdirection overlapping width less than 1/9λ; each moveable stage overlapswith at least one moveable stage in the stator-x direction or stator-ydirection with at least 2λ width; the overall size of the stator tile isnot greater than 9λ by 9λ; each moveable stage can be controlled in6-DOF.

While a number of exemplary aspects and embodiments are discussedherein, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. For example:

-   -   In this description and the accompanying claims, elements (such        as, by way of non-limiting example, stator layers, coil traces,        moveable stages and/or magnet arrays) are said to overlap one        another in or along a direction. For example, coil traces 32, 34        from different stator layers 40, 42 may overlap one another in        or along the stator-direction. When it is described that two or        more objects overlap in or along the z-direction, this usage        should be understood to mean that a z-direction-oriented line        could be drawn to intersect the two or more objects.    -   In many of the drawings and much of the description provided        herein, moveable stages are shown as being static with their        stage-x, stage-y and stage-z axes being the same as the        stator-x, stator-y and stator-z axes of the corresponding        stator. This custom is adopted in this disclosure for the sake        of brevity and ease of explanation. It will of course be        appreciated from this disclosure that a moveable stage can (and        is designed to) move with respect to its stator, in which case        the stage-x, stage-y, stage-z axes of the moveable stage may no        longer be the same as (or aligned with) the stator-x, stator-y        and stator-z axes of its stator. Directions, locations and        planes defined in relation to the stator axes may generally be        referred to as stator directions, stator locations and stator        planes and directions, locations and planes defined in relation        to the stage axes may be referred to as stage directions, stage        locations and stage planes.    -   In the description above, stators comprise current carrying coil        traces and moveable stages comprise magnet arrays. It is of        course possible that this could be reversed—i.e. stators could        comprise magnet arrays and moveable stages could comprise        current carrying coil traces. Also, whether a component (e.g. a        stator or a moveable stage) is actually moving or whether the        component is actually stationary will depend on the reference        frame from which the component is observed. For example, a        stator can move relative to a reference frame of a moveable        stage, or both the stator and the moveable stage can move        relative to an external reference frame. Accordingly, in the        claims that follow, the terms stator and moveable stage and        references thereto (including references to stator and/or stage        x, y, z-directions, stator and/or stage x, y, z-axes and/or the        like) should not be interpreted literally unless the context        specifically requires literal interpretation Moreover, unless        the context specifically requires, it should be understood that        the moveable stage (and its directions, axes and/or the like)        can move relative to the stator (and its directions, axes and/or        the like) or that the stator (and its directions, axes and/or        the like) can move relative to a moveable stage (and its        directions, axes and/or the like).    -   In this description and the accompanying claims, references are        made to controlling, controlling the motion of and/or        controlling the position of moveable stages in or with multiple        (e.g. 6) degrees of freedom. Unless the context or the        description specifically indicates otherwise, controlling,        controlling the motion of and/or controlling the position of        moveable stages in or with multiple degrees of freedom may be        understood to mean applying feedback position control in the        multiple degrees of freedom, but does not expressly require that        there be motion of moveable stage in any such degree of freedom

While a number of exemplary aspects and embodiments have been discussedabove, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. It is thereforeintended that the following appended claims and claims hereafterintroduced are interpreted to include all such modifications,permutations, additions and sub-combinations as are within their truespirit and scope.

What is claimed is:
 1. A method for moving a plurality of moveablestages relative to a stator, the method comprising: providing a statorcomprising one or more stator tiles, each stator tile comprising: anx-trace layer comprising a plurality of x-trace groups, each x-tracegroup comprising a plurality of electrically conductive x-traces whichextend in a stator-x direction across the stator tile and into whichcurrents may be independently driven; a y-trace layer comprising aplurality of y-trace groups, each y-trace group comprising a pluralityof electrically conductive y-traces which extend in a stator-y directionacross the stator tile and into which currents may be independentlydriven; the x-trace layer and the y-trace layer overlapping one anotherin a stator-z direction; the stator-x direction and the stator-ydirection non-parallel to one another; providing a plurality of moveablestages, each moveable stage comprising: a first magnet array comprisinga plurality of first magnetization segments linearly elongated in astage-x direction, each first magnetization segment having acorresponding magnetization direction orthogonal to the stage-xdirection and at least two of the first magnetization segments havingmagnetization directions that are different from one another; and asecond magnet array comprising a plurality of second magnetizationsegments linearly elongated in a stage-y direction, each secondmagnetization segment having a magnetization direction orthogonal to thestage-y direction and at least two of the second magnetization segmentshaving magnetization directions that are different from one another; athird magnet array comprising a plurality of third magnetizationsegments linearly elongated in the stage-x direction, each thirdmagnetization segment having a corresponding magnetization directionorthogonal to the stage-x direction and at least two of the thirdmagnetization segments having magnetization directions that aredifferent from one another; and the stage-x direction and the stage-ydirection non-parallel to one another; and driving currents in thex-traces and the y-traces to move a first moveable stage and a secondmoveable stage relative to the stator where the first magnet array ofthe first moveable stage overlaps with the first magnet array of thesecond moveable stage in the stator-x direction, wherein drivingcurrents in the x-traces and the y-traces to move the first moveablestage and the second moveable stage relative to the stator comprises:for at least a first portion of a time where the first magnet array ofthe first moveable stage overlaps with the first magnet array of thesecond moveable stage in the stator-x direction, controllably drivingfirst x-trace group currents in a first x-trace group that overlaps witha first portion of the first magnet array of the first moveable stage inthe stator-z direction and a first portion of the first magnet array ofthe second moveable stage in the stator-z direction, the first x-tracegroup currents determined based at least in part on positions of boththe first moveable stage and the second moveable stage and the firstx-trace group currents generating first forces on the first magnet arrayof the first moveable stage and on the first magnet array of the secondmoveable stage.
 2. A method according to claim 1 wherein drivingcurrents in the x-traces and the y-traces to move the first moveablestage and the second moveable stage relative to the stator comprises:for at least the first portion of the time where the first magnet arrayof the first moveable stage overlaps with the first magnet array of thesecond moveable stage in the stator-x direction, controllably drivingsecond x-trace group currents in a second x-trace group that overlapswith a second portion of the first magnet array of the first moveablestage in the stator-z direction and a second portion of the first magnetarray of the second moveable stage in the stator-z direction, the secondx-trace group currents determined based at least in part on positions ofboth the first moveable stage and the second moveable stage and thesecond x-trace group currents generating second forces on the firstmagnet array of the first moveable stage and on the first magnet arrayof the second moveable stage.
 3. A method according to claim 2comprising driving currents in the x-traces and the y-traces to move thefirst moveable stage and the second moveable stage relative to thestator where the third magnet array of the first moveable stage overlapswith the third magnet array of the second moveable stage in the stator-xdirection, wherein driving currents in the x-traces and the y-traces tomove the first moveable stage and the second moveable stage relative tothe stator comprises: for at least a first portion of a time where thethird magnet array of the first moveable stage overlaps with the thirdmagnet array of the second moveable stage in the stator-x direction,controllably driving third x-trace group currents in a third x-tracegroup that overlaps with a first portion of the third magnet array ofthe first moveable stage in the stator-z direction and a first portionof the third magnet array of the second moveable stage in the stator-zdirection, the third x-trace group currents determined based at least inpart on positions of both the first moveable stage and the secondmoveable stage and the third x-trace group currents generating firstforces on the third magnet array of the first moveable stage and on thethird magnet array of the second moveable stage.
 4. A method accordingto claim 3 wherein driving currents in the x-traces and the y-traces tomove the first moveable stage and the second moveable stage relative tothe stator comprises: for at least the first portion of the time wherethe third magnet array of the first moveable stage overlaps with thethird magnet array of the second moveable stage in the stator-xdirection, controllably driving fourth x-trace group currents in afourth x-trace group that overlaps with a second portion of the thirdmagnet array of the first moveable stage in the stator-z direction and asecond portion of the third magnet array of the second moveable stage inthe stator-z direction, the fourth x-trace group currents determinedbased at least in part on positions of both the first moveable stage andthe second moveable stage and the fourth x-trace group currentsgenerating second forces on the third magnet array of the first moveablestage and on the third magnet array of the second moveable stage.
 5. Amethod according to claim 1 wherein driving currents in the x-traces andthe y-traces to move the first moveable stage and the second moveablestage relative to the stator comprises: for at least a second portion ofthe time where the first magnet array of the first moveable stageoverlaps with the first magnet array of the second moveable stage in thestator-x direction, refraining from driving currents in the firstx-trace group.
 6. A method according to claim 2 wherein driving currentsin the x-traces and the y-traces to move the first moveable stage andthe second moveable stage relative to the stator comprises: for at leasta second portion of the time where the first magnet array of the firstmoveable stage overlaps with the first magnet array of the secondmoveable stage in the stator-x direction, refraining from drivingcurrents in the first x-trace group; and for at least the second portionof the time where the first magnet array of the first moveable stageoverlaps with the first magnet array of the second moveable stage in thestator-x direction, refraining from driving currents in the secondx-trace group.
 7. A method according to claim 2 wherein driving currentsin the x-traces and the y-traces to move the first moveable stage andthe second moveable stage relative to the stator comprises: for at leasta second portion of the time where the first magnet array of the firstmoveable stage overlaps with the first magnet array of the secondmoveable stage in the stator-x direction, driving currents in the firstx-trace group and the second x-trace group which are the same as oneanother.
 8. A method according to claim 4 wherein driving currents inthe x-traces and the y-traces to move the first moveable stage and thesecond moveable stage relative to the stator comprises: for at least asecond portion of the time where the first magnet array of the firstmoveable stage overlaps with the first magnet array of the secondmoveable stage in the stator-x direction, driving currents in the firstx-trace group and the second x-trace group which are the same as oneanother; and for at least a second portion of the time where the thirdmagnet array of the first moveable stage overlaps with the third magnetarray of the second moveable stage in the stator-x direction, drivingcurrents in the third x-trace group and the fourth x-trace group whichare the same as one another.
 9. A method according to claim 1 whereindriving currents in the x-traces and the y-traces to move the firstmoveable stage and the second moveable stage relative to the statorcomprises, during the first portion of the time where the first magnetarray of the first moveable stage overlaps with the first magnet arrayof the second moveable stage in the stator-x direction, driving currentsin the x-traces and the y-traces which control motion of the firstmoveable stage with six degrees of freedom and which control motion ofthe second moveable stage with six degrees of freedom.
 10. A methodaccording to claim 3 wherein driving currents in the x-traces and they-traces to move the first moveable stage and the second moveable stagerelative to the stator comprises, during the first portion of the timewhere the third magnet array of the first moveable stage overlaps withthe third magnet array of the second moveable stage in the stator-xdirection, driving currents in the x-traces and the y-traces whichcontrol motion of the first moveable stage with six degrees of freedomand which control motion of the second moveable stage with six degreesof freedom.
 11. A method according to claim 1 wherein, during the firstportion of the time where the first magnet array of the first moveablestage overlaps with the first magnet array of the second moveable stagein the stator-x direction, the positions of the first moveable stage andthe second moveable stage satisfy a condition 0<η₁<η₁*, where: η₁ is afirst magnet array overlap factor which represents a fraction of thewidths W_(my) of the first magnet arrays of the first and secondmoveable stages that overlap with one another in the stator-x direction;and η₁* is a first overlap threshold.
 12. A method according to claim 11wherein the first magnet array overlap factor η₁ is represented by afraction 0<η₁≤1 and the first overlap threshold η₁* is greater than 0.5.13. A method according to claim 11 comprising, during the first portionof the time where the first magnet array of the first moveable stageoverlaps with the first magnet array of the second moveable stage in thestator-x direction, determining the first x-trace group currents basedon a proportion (1−η₁/2) of a stage-y dimension of the first magnetarray of the first moveable stage that overlaps with the first x-tracegroup in the stator-z direction and based on a proportion η₁/2 of astage-y dimension of the first magnet array of the second moveable stagethat overlaps with the first x-trace group in the stator-z direction.14. A method according to claim 11 wherein, during the first portion ofthe time where the first magnet array of the first moveable stageoverlaps with the first magnet array of the second moveable stage in thestator-x direction, the first magnet array overlap factor m isincreasing over time.
 15. A method according to claim 11 comprisingdetermining the first magnet array overlap factor η₁ based on positionfeedback.
 16. A method according to claim 3 wherein during the firstportion of the time where the third magnet array of the first moveablestage overlaps with the third magnet array of the second moveable stagein the stator-x direction, the positions of the first moveable stage andthe second moveable stage satisfy a condition 0<η₃<η₃*, where: η₃ is athird magnet array overlap factor which represents a fraction of thewidths W_(my) of the third magnet arrays of the first and secondmoveable stages that overlap with one another in the stator-x direction;and Θ₃* is a third overlap threshold.
 17. A method according to claim 1wherein, during the first portion of the time where the first magnetarray of the first moveable stage overlaps with the first magnet arrayof the second moveable stage in the stator-x direction, determining thefirst x-trace group currents based on a proportion (1−η₁/2) of a stage-ydimension of the first magnet array of the first moveable stage thatoverlaps with the first x-trace group in the stator-z direction andbased on a proportion η₁/2 of a stage-y dimension of the first magnetarray of the second moveable stage that overlaps with the first x-tracegroup in the stator-z direction.
 18. A method according to claim 1wherein, during the first portion of the time where the first magnetarray of the first moveable stage overlaps with the first magnet arrayof the second moveable stage in the stator-x direction, a first magnetarray overlap factor η₁ is increasing, the first magnet array overlapfactor η₁ representing a fraction of the widths W_(my) of the firstmagnet arrays of the first and second moveable stages that overlap withone another in the stator-x direction.
 19. A method according to claim17 comprising determining the first magnet array overlap factor η₁ basedon position feedback.
 20. A method according to claim 5 wherein: duringthe first portion of the time where the first magnet array of the firstmoveable stage overlaps with the first magnet array of the secondmoveable stage in the stator-x direction, the positions of the firstmoveable stage and the second moveable stage satisfy a condition0<η₁<η₁*, where: η₁ is a first magnet array overlap factor whichrepresents a fraction of the widths W_(my) of the first magnet arrays ofthe first and second moveable stages that overlap with one another inthe stator-x direction; and η₁* is a first overlap threshold; and duringthe second portion of the time where the first magnet array of the firstmoveable stage overlaps with the first magnet array of the secondmoveable stage in the stator-x direction, the positions of the firstmoveable stage and the second moveable stage satisfy a conditionη₁*≤η₁≤1 where η₁ is the first magnet array overlap factor.